A better question is: Is Tradition also a medium of divinely revealed truth?
If so, then it is on par with Holy Scripture.
First, is the Word of God intrinsically something which is written word?
Scripture itself calls the oral teaching of the Apostles, under inspiration of the Holy Ghost, the Word of God. We know, therefore, that the Word of God cannot be said to be exclusively, or intrinsically, written, at least necessarily:
1 Thessalonians 2:13
Therefore we give thanks to God without ceasing: because that when you had received of us the word of the hearing of
God you received it not as the word of men but (as it is indeed) the
word of God, who worketh in you that have believed.
So the answer is no, the Word of God can be preached and still remain to be the Word of God (if you took Scripture away after you had preached it, you would have nonetheless preached the Word of God [1 Cor 15:2], proving its written component being accidental, in the 'consequence' or philisophical sense).
The Apostles also conveyed revelation in the form of Tradition: oral, i.e. handed-on, teachings which are to be held to be the truth just as the epistles are held to be truth in the Church.
2 Thessalonians 2:15
Therefore, brethren, stand fast; and hold the traditions which you have learned, whether by word*, or by our epistle.
* spoken word
This further and concretely and explicitly tells us the Word of God is both Scripture and Tradiiton. Since here, Tradition is defined as epistle (written Word of God) and oral Tradition (not a game of telephone—teaching that was simply not written teaching, but which was to nonetheless form the faith of the Church in the same way).
Since oral and written epistle form are two veins of the one term 'Tradition', or, as we might say 'deposit of faith', we cannot only accept one or the other—you'll notice the 'or' here does not have that meaning; it isn't a choice between the oral tradition and the written. We are to hold fast to both. Written Scripture is merely the crystalized Tradition, or Word of God, as oral Tradiiton is.
They would not be distinguished like this if only the written Word is the Word of God.
In Matthew 28:20 we read that Christ taught His disciples to teach everything He had commanded. Yet we read twice in John's Gospel that Christ's actions were not all written down (Jn 21:25). In fact, he uses strong hypberbole to convey this point: all the world could not contain all that could be written of what Jesus said and did.
Asking if removing something will not change anything that will affect your salvation is to question the validity of giving that Tradition in the first place. Did St. Paul suggest tradition, or did he hand it on to be believed just as the rest of his epistles were (1 Cor 11:2)?
Is the light of a fire sufficient enough to constitute a fire? No, it by definition causes the heat. Asking if the the light alone is sufficient is to question the nature of fire. Similarly, questioning the oral and written components of the Word of God is to do the same; namely, question the nature of divine revelation.
As we saw from Scripture, the Word of God, the Tradition or deposit of faith handed on through the Apostles, is both written and oral in nature.
Some Protestants argue that Scripture itself says Scripture alone is sufficient. In reality, any supposed Scriptural evidence neglect or ignore one simple fact: none of the provided texts are actually exclusive.
For one example,
2 Timothy 3:16-17
All scripture, inspired of God, is profitable to teach, to reprove, to
correct, to instruct in righteousness, that the man of God may be
perfect, furnished to every good work.
Notice what this says: all of the Scripture is inspired. It is helpful for (profitable, helpes toward the end of—) making you able or equiped for ever good work.
It doesn't say only Scripture is inspired. It doesn't say that it exclusively achieves the benefits described.
To make matters worse, it doesn't even include the New Testament, since they didn't exist in its entirety when this was written. It referred to the Tanakh, or Old Testament.
In fact, the same is said to result or be the benefit of purging oneself of bad works (2 Timothy 2:21).
The faith does not only consist in reading the Scriptures, but interpreting them (which itself implies access to an orthodox interpretation of the Church—including and taking into consideration Tradition), applying it (the same applies here), living it.