Toady posted a reply on the DF forum which addresses your question:
If the civ's knowledge is all the way up at domesticated, the animal becomes Tame as before and never reverts. As it stands, you can't yet cross the boundary to domesticated from a wild beast, since there's extra infrasture to be dealt with with breeds and all that. Children inherit their training status from their parents, and if a trainer gets to an animal when it is young, it becomes Tame and never reverts. The word "trained" is somewhat weird that way. It doesn't refer to how many tricks the animal knows, but more how acclimated it is to dwarven life. So a "masterfully trained" animal will have "masterfull trained" children which can be raised up to tame if you catch them early, but after some years of complete inattention, the masterfully trained parent can revert back down the ladder all the way to semi-wild and wild. Tame creatures will have tame children that never need basic training. So you can eventually get up to a population that is essentially domestic, with your trained exotics having trained children which are tamed and then have tamed children for all generations after that. However, this won't give you "domestic" civ knowledge -- which means that a new exotic of that species which you capture will still have to be trained and reinforced (instead of jumping up to Tame).
Source: Future of the Fortress reply
So in answer to your question, you can fully domesticate animals in fortress mode, but you have to tame them as children in order to stop them reverting back to a wild state.
Another quote from Toady to back this up:
My voracious cave crawler trainer was killed by trogs, and I was
fussing with some clothing issue or another, so I didn't notice. The
cave crawler eventually reverted and killed half of my dwarves. I
caught it in a cage trap and rehabilitated it, but the damage was
done. Zach bred and trained raccoons, culminating with a battle with a
blind cave ogre. He trained the second generation of raccoons while
they were young, so they became fully tame without risk of reversion.
Source: DF Current Development Feed (22nd March 2012)