According to Roman Catholic doctrine, does the incorruptible body possess blood?

Eucharistic wine is true blood of Christ, in a mystical sense. It is not actual, physical blood.

It is actual blood in essence, ie, in what it means - life, total self giving. Eucharist is a memory of the actual historical sacrifice, and a continuing, complete self giving of Jesus to us.

A sign is something that is not what it is showing/pointing to. A sign is worthless in it self. In this meaning, Eucharist is not a sign. In contrast to this meaning, Eucharist IS blood and body of Christ.

In this mystical meaning, your question does not apply. Ie, Catholics do not believe that Christ is continually cutting Himself daily to give us a little of his blood, so the question of weather His current body has or has no blood, in relation to Eucharist is meaningless.

Ie, the belief that Eucharist is both blood and body of Christ and bread and wine, is a mystery similar to the Trinity.

Hope this makes a bit of sense :)

Transubstantiation is the real change of bread and wine into the body and blood of Christ; but to answer this question it is important to understand that during Mass we are celebrating the same Passover meal with Christ in which he instructed us to do this.

God is not bound by time and space.

In that way, we are eating the body and drinking the blood but it is the body and blood of Christ prior to his resurrected body. We are there, at that last meal when Christ said "this is my body...this is my blood."

This is what is meant in the Catechism of the Catholic Church paragraphs #1363 and 1364: "In the sense of Sacred Scripture the memorial is not merely the recollection of past events but the proclamation of the mighty works wrought by God for men. In the liturgical celebration of these events, they become in a certain way present and real. This is how Israel understands it liberation from Egypt: every time Passover is celebrated, the Exodus events are made present...When the Church celebrates the Eucharist, she commemorates Christ's Passover, and it is made present..."

Thus, whether or not a incorruptible body possesses blood makes no difference during transubstantiation nor does it affect the real body and blood we consume during Mass since we are right there with Christ and, for that matter, also with all Masses yet to be celebrated.

Regarding whether Christ's entire body—with its flesh, blood, etc.—rose in His resurrection, St. Thomas Aquinas writes (Summa Theologica III q. 54 a. 3):

Objection 1: It would seem that Christ's body did not rise entire. For flesh and blood belong to the integrity of the body: whereas Christ seems not to have had both, for it is written (1 Cor. 15:50): "Flesh and blood can not possess the kingdom of God." But Christ rose in the glory of the kingdom of God. Therefore it seems that He did not have flesh and blood.

Objection 2: Further, blood is one of the four humors. Consequently, if Christ had blood, with equal reason He also had the other humors, from which corruption is caused in animal bodies. It would follow, then, that Christ's body was corruptible, which is unseemly. Therefore Christ did not have flesh and blood.

Objection 3: Further, the body of Christ which rose, ascended to heaven. But some of His blood is kept as relics in various churches. Therefore Christ's body did not rise with the integrity of all its parts.

On the contrary, our Lord said (Lk. 24:39) while addressing His disciples after the Resurrection: "A spirit hath not flesh and bones as you see Me to have."

I answer that, As stated above (Article [2]), Christ's body in the Resurrection was "of the same nature, but differed in glory." Accordingly, whatever goes with the nature of a human body, was entirely in the body of Christ when He rose again. Now it is clear that flesh, bones, blood, and other such things, are of the very nature of the human body. Consequently, all these things were in Christ's body when He rose again; and this also integrally, without any diminution; otherwise it would not have been a complete resurrection, if whatever was lost by death had not been restored. Hence our Lord assured His faithful ones by saying (Mt. 10:30): "The very hairs of your head are all numbered": and (Lk. 21:18): "A hair of your head shall not perish."

But to say that Christ's body had neither flesh, nor bones, nor the other natural parts of a human body, belongs to the error of Eutyches, Bishop of Constantinople, who maintained that "our body in that glory of the resurrection will be impalpable, and more subtle than wind and air: and that our Lord, after the hearts of the disciples who handled Him were confirmed, brought back to subtlety whatever could be handled in Him" [*St. Gregory, Moral. in Job 14:56]. Now Gregory condemns this in the same book, because Christ's body was not changed after the Resurrection, according to Rm. 6:9: "Christ rising from the dead, dieth now no more." Accordingly, the very man who had said these things, himself retracted them at his death. For, if it be unbecoming for Christ to take a body of another nature in His conception, a heavenly one for instance, as Valentine asserted, it is much more unbecoming for Him at His Resurrection to resume a body of another nature, because in His Resurrection He resumed unto an everlasting life, the body which in His conception He had assumed to a mortal life.

Reply to Objection 1: Flesh and blood are not to be taken there for the nature of flesh and blood, but, either for the guilt of flesh and blood, as Gregory says [*St. Gregory, Moral. in Job 14:56], or else for the corruption of flesh and blood: because, as Augustine says (Ad Consent., De Resur. Carn.), "there will be neither corruption there, nor mortality of flesh and blood." Therefore flesh according to its substance possesses the kingdom of God, according to Lk. 24:39: "A spirit hath not flesh and bones, as you see Me to have." But flesh, if understood as to its corruption, will not possess it; hence it is straightway added in the words of the Apostle: "Neither shall corruption possess incorruption."

Reply to Objection 2: As Augustine says in the same book: "Perchance by reason of the blood some keener critic will press us and say; If the blood was" in the body of Christ when He rose, "why not the rheum?" that is, the phlegm; "why not also the yellow gall?" that is, the gall proper; "and why not the black gall?" that is, the bile, "with which four humors the body is tempered, as medical science bears witness. But whatever anyone may add, let him take heed not to add corruption, lest he corrupt the health and purity of his own faith; because Divine power is equal to taking away such qualities as it wills from the visible and tractable body, while allowing others to remain, so that there be no defilement," i.e. of corruption, "though the features be there; motion without weariness, the power to eat, without need of food."

Reply to Objection 3: All the blood which flowed from Christ's body, belonging as it does to the integrity of human nature, rose again with His body: and the same reason holds good for all the particles which belong to the truth and integrity of human nature. But the blood preserved as relics in some churches did not flow from Christ's side, but is said to have flowed from some maltreated image of Christ.