If you mean variants that produce a meaningful variation in the English then, yes, that would be useful. Is that what you are aiming for?
The rest of this I write partly from a YouTube video of a lecture by my current favorite textual critic, Daniel Wallace entitled "How badly was the New Testament corrupted?"
From 29 minutes into the video:
There are just over 138,000 words in the Greek New Testament, and 500,000 Greek textual variants. I believe there are about 5,800 ancient Greek manuscripts producing these half a million variants.
This means there are (about) 3.5 textual variants for every word in the NT, or a verse of say 15 words would have over 50 textual variants.
At first sight this is a bit worrying.
Perhaps you should see the video to find out why it is not only not worrying, but actually good news.
But what it does mean is that it is entirely pointless, and impossibly cumbersome, to have all the Greek variants for the Textus Receptus. If you mean you want all the variants for the few manuscripts which Erasmus et al worked, then the question would obviously be: Why do you want just these Greek manuscripts and not others?
But which textus receptus do you mean? The reason I ask can be seen from the wikipedia entry under "Textus Receptus".
John Mill (1645-1707) worked on 82 manuscripts and came up with about 30,000 variants in the Greek, in "Novum Testamentum Graecum". Today, I believe we have 5,800 ancient Greek manuscripts, nearly all portions of the NT, mostly small portions.
It is really not possible or useful to produce a Bible with all the variants. Most variants make no difference whatsoever to the English translation. Daniel Wallace in another youtube video shows there are thousands of ways to write the Greek for "John loves Mary": all are equally accurate in the Greek.
The somewhat alarming situation of the multiple variations of the Greek of the NT can be compared with the situation for the Qu'ran, which Moslems claim is so much better because they claim there is only one version of the Qu'ran in existence today. This claim is today being challenged as never before: see the work of Qu'ranic textual critic, Dan Brubaker, at www.danielbrubaker.com.
Let us suppose that in fact it is true, there is only one ancient Arabic version of the Qu'ran. Does this prove that this ancient version is the original version? Does it prove that Muslims, in this version, have the Word of (their) prophet, and (their) God? Of course, it does not prove it at all. It could be completely different from what was said by Mohammed and what was first written down by his followers. It could also mean that an early Muslim sought out all the variations of the Qu'ran, produced a single version which attempted to harmonise all the variants, and then burned the variants: but how would anyone know today that the harmonisation was a good one? We would not and could never know. (If you read (free, online) volume 6, book 61 of Hadith Bukhari (the most accepted authoritative Hadith of all) what I have just written is exactly what happened (Bukhari,vol 6,book 61, verse510). Khalifa Uthman ordered the burning. For him Unity amongst Muslims was more important than Truth. Having unity was more important than having a clear knowledge of the words of their prophet, and presumably what God had said through him. (Nevertheless, there are multiple variations in the Qu'ran today as argued by Jay Adams.)
Now consider the case with the Bible and its half a million variant readings. What we can FIRSTLY learn is there was no conspiracy or politically motivated attempt to produce a single version with no variants. There were no bonfires of variant readings in the early church: praise God! In the early Church there was no prioritising unity amongst Christians above the preservation of all variant readings, praise God: we have a rich tapestry of variant readings, from which textual critics can try to get us back to what is likely the original Word. No one in the early church had sufficient political power to enforce any bonfires, or to try to enforce the suppression of variants, praise God. (Nor, as far as we know, was there any desire or any arrogant claim to know which was the original.) The NT scriptures had spread out very quickly across many countries. Suppression was not possible without political power, and there was no political power across so many countries. Also there is no record of such suppression in the historical accounts: it simply does not exist, because it never happened, and we have 500,000 variant readings to prove it!
SECONDLY, for Christians Truth is important! What God has said is more important than anything else. It is more important than unity amongst Christians.
THIRDLY, the variants make no difference to any essential Christian doctrine: Bart Ehrman, the world's leading atheist Biblical textual critic, trained by Bruce Metzger, has said as much. From Christianapologetics.org
Interviewer: "Bruce Metzger, your mentor in textual criticism to whom this book is dedicated, has said that there is nothing in these variants of Scripture that challenges any essential Christian beliefs (e.g. the bodily resurrection of Jesus or the Trinity). Why do you believe these core tenets of Christian orthodoxy to be in jeopardy based on the scribal errors you discovered in the biblical manuscripts?"
Bart Ehrman: “Bruce Metzger is one of the great scholars of modern times, and I dedicated the book to him because he was both my inspiration for going into textual criticism and the person who trained me in the field. And even though we may disagree on important religious questions—he is a firmly committed Christian and I am not—we are in complete agreement on a number of very important historical and textual questions. If he and I were put in a room and asked to hammer out a consensus statement on what we think the original text of the New Testament probably looked like, there would be very few points of disagreement—maybe one or two dozen places out of many thousands.
The position I argue for in Misquoting Jesus does not actually stand at odds with Prof. Metzger’s position that the essential Christian beliefs are not affected by textual variants in the manuscript tradition of the New Testament. What he means by that (I think) is that even if one or two passages that are used to argue for a belief have different textual reading, there are still other passages that could be used to argue for the same belief. For the most part, I think that’s true.
But I was looking at the question from a different angle. My question is not about traditional Christian beliefs, but about how to interpret passages of the Bible. And my point is that if you change what the words say, then you change what the passage means. Most textual variants (Prof. Metzger and I agree on this) have no bearing at all on what a passage means. But there are other textual variants (we agree on this as well) that are crucial to the meaning of a passage. And the theology of entire books of the New Testament are sometimes affected by the meaning of individual passages.
From my point of view, the stakes are rather high: Does Luke’s Gospel teach a doctrine of atonement (that Christ’s death atones for sins)? Does John’s Gospel teach that Christ is the “unique God” himself? Is the doctrine of the Trinity ever explicitly stated in the New Testament? These and other key theological issues are at stake, depending on which textual variants you think are original and which you think are creations of early scribes who were modifying the text.”
Bart Ehrman, Misquoting Jesus (New York: HarperSanFrancisco, 2005), 252-3, Emphasis added.
FOURTHLY, we have two helps to help us identify which variants are true. Where a variant is clearly contrary to the rest of God's Word, where it is a single variant with all other variants unified in the text, where it exists in a much larger work which is otherwise clearly doctrinally dubious: all these help. The Holy Spirit guides the believer into all truth. The textual critics that are Christian are also so guided.
FIFTHLY, there are only three passages in the NT that are suspicious enough to be highlighted (or even omitted) in modern versions, John 7:53-8:11, Mark 16:9-20, and the different rendering of 1st John 5:7-8. None of these are critical for essential Christian doctrine. The trinity in 1st John 5:7,8 can be found elsewhere.