There does not seem to be a clear statement from the Reformed tradition whether the words as written by Paul to the Corinthians are to be taken literally. Most of the Reformed statements concerning this verse are addressed to current believers. In this case, the concesus seems to be that the words are to be understood as spiritual but literal -- that profaning the Lord's Supper will result in condemnation and spiritual death.
We begin with Calvin. His views are not necessarily binding on the Reformed, but it is difficult to ignore his thoughts when discussing Reformed theology. Calvin's commentary on Corinthians shows that he believed the Corinthians were quite literally and physically suffering sickness and death for their actions:
[Paul] now instructs the Corinthians as to the chastisement which they were at that time enduring. It is not known whether a pestilence was raging there at that time, or whether they were laboring under other kinds of disease. However it may have been as to this, we infer from Paul's words, that the Lord had sent some scourge upon them for their correction. Nor does Paul merely conjecture, that it is on that account that they are punished, but he affirms it as a thing that was perfectly well known by him. He says, then, that many lay sick --- that many were kept long in a languishing condition, and that many had died, in consequence of that abuse of the Supper, because they had offended God.
After denouncing the Catholic Church for her practices concerning the Lord's Supper, Calvin goes on to suggest that the Reformed are not honoring Christ in the Supper as fully as they should. He states that current wars, plagues, and famines are due to hypocracy and irreverence concerning the Supper:
Nay even among ourselves, who have the pure administration of the Supper restored to us, in virtue of a return, as it were, from captivity, how much irreverence! How much hypocrisy on the part of many! What a disgraceful mixture, while, without any discrimination, wicked and openly abandoned persons intrude themselves, such as no man of character and decency would admit to common intercourse! And yet after all, we wonder how it comes that there are so many wars, so many pestilences, so many failures of the crop, so many disasters and calamities --- as if the cause were not manifest!
Note that this guilt seems to collectively affect both the innocent and guilty. This seems to be consistent with Calvin's speculation that the Corinthians may have been enduring a plague. However, in his Institutes of the Christian Religion (and this may be seen as a more 'official' stance), Calvin focuses the spiritual effects of eating and drinking the Supper unworthily. These concequences are limited to the unrighteous only in which the condemn themselves:
For, inasmuch as they do not believe that body to be their life, they put every possible affront upon it, stripping it of all its dignity, and profane and contaminate it by so receiving; inasmuch as while alienated and estranged from their brethren, they dare to mingle the sacred symbol of Christ's body with their dissensions. No thanks to them if the body of Christ is not rent and torn to pieces. Wherefore they are justly held guilty of the body and blood of the Lord, which, with sacrilegious impiety, they so vilely pollute. By this unworthy eating, they bring judgment on themselves. For while they have no faith in Christ, yet, by receiving the sacrament, they profess to place their salvation only in him, and abjure all other confidence. Wherefore they themselves are their own accusers; they bear witness against themselves; they seal their own condemnation. (Institutes vi.xviii.xl)
Moving on from Calvin, we focus on some of the classical statements of the Reformed tradition: the Belgic Confession and the Heidelberg Catechism. These documents represent the formalization of the Reformed Christianity as practiced on Continental Europe during the Reformation. They are still respected and used by Reformed groups today. Neither of these can be said to diffinitively rule out a literal physical effect, but a real spiritual effect seems more likely -- more consitent with Calvins Institutes rather than his commentary.
The Belgic Confession
The Belgic Confession explains in Article 35 does not expand much on the effects of receiving the Supper unworthily, but it is consistent with real, spiritual effect:
The wicked person certainly takes the sacrament, to his condemnation, but does not receive the truth of the sacrament, just as Judas and Simon the Sorcerer both indeed received the sacrament, but not Christ, who was signified by it. He is communicated only to believers...Therefore no one should come to this table without examining himself carefully, lest "by eating this bread and drinking this cup he eat and drink to his own judgment."
The Heidelberg Catechism
The Heidelberg Catechism does not say much more than restate Scripture:
Question 81. For whom is the Lord's supper instituted?
Answer. For those who are truly sorrowful for their sins, and yet trust that these are forgiven them for the sake of Christ; and that their remaining infirmities are covered by his passion and death; and who also earnestly desire to have their faith more and more strengthened, and their lives more holy; but hypocrites, and such as turn not to God with sincere hearts, eat and drink judgment to themselves.
If we place this question in the context of the one before it we see that the benefits are spiritual:
Question 80. What difference is there between the Lord's supper and the popish mass?
Answer. The Lord's supper testifies to us, that we have a full pardon of all sin by the only sacrifice of Jesus Christ, which he himself has once accomplished on the cross; and, that we by the Holy Ghost are ingrafted into Christ, who, according to his human nature is now not on earth, but in heaven, at the right hand of God his Father, and will there be worshipped by us. But the mass teaches....
The benefits, full pardon and ingrafting, are spiritual. It seems reasonable in lack of evidence to the contrary to understand the consequences are spiritual too.
The Westminster Confession of Faith
Finally we turn to the The Westminster Confession of Faith. This document originated in the Church of England, but is now primarily associated with Presbyterian groups within the Reformed Tradition. Its statements are similar to the Belgic and Heidelberg, it is a little more explicit:
Although ignorant and wicked men receive the outward elements in this sacrament; yet, they receive not the thing signified thereby; but, by their unworthy coming thereunto, are guilty of the body and blood of the Lord, to their own damnation. Wherefore, all ignorant and ungodly persons, as they are unfit to enjoy communion with Him, so are they unworthy of the Lord's table; and cannot, without great sin against Christ, while they remain such, partake of these holy mysteries, or be admitted thereunto.
While the other documents spoke of judgment and condemnation, the WCF states that receiving the Supper in an unworthy manner is a great sin and brings damnation.
The Reformed tradition understands the warnings of sickness and death in 1 Corinthians 11 to indicate serious spiritual death and damnation.