Once entered into slavery, they have a semi-conversion whereupon they must keep a certain set of limited rules. Can they choose to fully convert and then be freed at the appropriate time of Shmita and Yovel?
They might be able to fully convert at the original time. Once they have entered into slavery, however, all the laws of עבד כנעני apply. They cannot escape that status voluntarily.
In any case, no slave regains his freedom at Shmita. All slaves (except a Canaanite) regain their freedom at Yovel, but the only ones whose freedom is bound only to Yovel is (a) the עבד נרצע, a Jewish manservant whose six years (not Shmita!) have expired but chooses to remain by having his ear punctured, and (b) the נמכר לעכום, one who has sold himself to a non-Jew. (Actually, the latter can also buy his freedom, either himself or through a relative.)