The Catholic Church certainly teaches that the good thief—often traditionally called St. Dismas—did in fact merit and receive salvation:
The parable of the poor man Lazarus and the words of Christ on the cross to the good thief, as well as other New Testament texts speak of a final destiny of the soul—a destiny which can be different for some and for others.
(Catechism of the Catholic Church, paragraph 1021; emphasis added)
As for when this occurred:
Each man receives his eternal retribution in his immortal soul at the very moment of his death, in a particular judgment that refers his life to Christ: either entrance into the blessedness of heaven—through a purification or immediately,—or immediate and everlasting damnation.
(Catechism paragraph 1022; emphasis added)
Of course, after death, it's arguable that time doesn't have much meaning; so asking whether after death someone was "in heaven" on the 14th of the month or not until later, or asking how long someone spends in Purgatory, probably doesn't make sense. That being the case, Catholic commentators seem to have argued that it is best to believe that indeed the thief was in Heaven as soon as Jesus died. Richard Challoner, who revised and edited the Catholic Douay-Rheims Bible, stated in a footnote to the passage:
Christ was pleased, by a special privilege, to reward the faith and confession of the penitent thief, with a full discharge of all his sins, both as to the guilt and punishment; and to introduce him immediately after death into the happy society of the saints, whose limbo, that is, the place of their confinement, was now made a paradise by our Lord's going thither.