The issue is the use of the words substance and substantial, and applying a modern meaning to them.
The Catechism of the Catholic Church, following the doctrine expounded at the Council of Trent, says
1376 The Council of Trent summarizes the Catholic faith by declaring: "Because Christ our Redeemer said that it was truly his body that he was offering under the species of bread, it has always been the conviction of the Church of God, and this holy Council now declares again, that by the consecration of the bread and wine there takes place a change of the whole substance of the bread into the substance of the body of Christ our Lord and of the whole substance of the wine into the substance of his blood. This change the holy Catholic Church has fittingly and properly called transubstantiation."206
But just because the "substance" of the bread is changed into the "substance" of the Body, and the "substance" of the wine is changed into the "substance" of the Blood, it doesn't mean that the species of the bread has changed. It's still bread; and the wine is still wine.
St Cyril of Jerusalem (313–386) wrote in his Catecheses, quoted by Pope Paul VI in Mysterium Fidei:
Instructed as you are in these matters, and filled with an unshakeable faith that what seems to be bread is not bread — though it tastes like it — but rather the Body of Christ; and that what seems to be wine is not wine — even though it too tastes like it — but rather the Blood of Christ … draw strength from receiving this bread as spiritual food and your soul will rejoice.
Catecheses, 22.9 [myst. 4] PG 33.1103
All the documents of the Church are written in Latin and then translated into other languages. In recent years, there has been a tendency to use Latinate words in English which are cognate with the original Latin text, even though their meaning has shifted since they were originally adopted in English. This particularly afflicts substance which came to English from Norman French, where it had already acquired a different nuance of meaning from Classical Latin. OED has, in its etymology:
physical existence, matter, (in theology) essence (all late 12th cent.)
classical Latin substantia ... underlying or essential nature ...
By the late twelfth century, substance had a meaning very close to its modern English meaning. But the Latin substantia, which is translated as substance, means something different. Thus it's wrong to impute a physicality of flesh to the bread, or of blood to the wine. But even though the bread remains in its species of bread, it nevertheless becomes, in its underlying or essential nature, the Body of Christ (perhaps it might even be said to have two natures in much the same way as Jesus himself had two natures in hypostatic union). The Church teaches transubstantiation; it does not teach transpeciation, where bread is changed into meat.
It is in this way that
The Eucharistic presence of Christ begins at the moment of the consecration and endures as long as the Eucharistic species subsist. Christ is present whole and entire in each of the species and whole and entire in each of their parts, in such a way that the breaking of the bread does not divide Christ.207
The Eucharistic presence of Christ is not derived from his glorious body (which may or may not have blood): it's derived from his earthly body, which definitely was flesh and blood.
CCC 1367 The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice: "The victim is one and the same: the same now offers through the ministry of priests, who then offered himself on the cross; only the manner of offering is different."190
It is Christ's offering of his earthly self on the Cross which is united with the offering on the altar.
Now, this may not actually answer the question "Does the incorruptible body possess blood?" but that's because it answers the secondary question "How can Roman Catholics drink Jesus' blood in the Eucharist?" The Eucharist does not depend on the nature of the incorruptible body.
190 Council of Trent (1562) Doctrina de ss. Missae sacrificio, c. 2: DS 1743; cf. Heb 9:14,27.
206 Council of Trent (1551): DS 1642; cf. Mt 26:26 ff.; Mk 14:22 ff.; Lk 22:19 ff.; 1 Cor 11:24 ff.
207 Cf. Council of Trent: DS 1641.