"In Communist Himalayas, Yeti trains you!", to badly morph the meme.
However, there's always the possibility of changing your Raw tags.
IRL, it seems that proto-dog-like wolves 'trained' early humans, as much as humans 'trained' the wolves. But that's a complex issue. Modern attempts at wolf-training are quite concerted efforts, or involve breeding them into dog germ-lines to get wolfier-than-dogs, doggier-than-wolves offspring.
(Or, like with a certain Russian experiment, not with wolves but another normally wild species, is a matter of mass-breeding a certain type of wild animal segregating (and inter-breeding only among their own set) those that exhibit human-friendly behaviour from those that exhibit human-hostile behaviour... With the interesting side-effect that the physiognomy of the 'friendly' line changes to simultaneously give them the same "puppy dog" features (even though being non-canine!). Indicating some link (if one can perhaps exclude experimenter bias of attitude, that creeps into the selection process) between the physical phenotype and the mental make-up, in those genetic switches. "Puppyfication", perhaps, in keeping them mentally/physically infantile, compared to their wild-attitude brethren?)
But, back to DF, the recent changes made training more prevalent (but graded by difficulty, according to familiarity) and perhaps everything should be trainable, in the right circumstances... Yes, this probably means "Fido, the Ampersand" should be possible, albeit very difficult. That is unless (and I'm not too sure about this detail) it'd have the [SENTIENT] quality.
(But how about a 'young' [SENTIENT], not that there's that many Ampersands but there are others of other races, being adopted. Which also leads to the possibility of feral infant [SENTIENT]s having a small chance of 'adopted' by a wild animal. Would add a bit of variety to find feral dwarf-children raised by wolves, or feral elven ones raised by anteaters, or somesuch... There's already the mechanics of Goblin kidnap and re-raising as Goblins, which can be re-tasked or developed for more global use whenever a sufficiently young other-race infant is encountered. Probably needs to be limited to social/pack animals. A "Feral 'desert scorpion'-child" doesn't sound so likely... But... possible? Ahem, but I drift off of the original topic, somewhat.)
 I think it's still something that can be changed without re-worldgenning. It's how I got War Elephants, but that was back in 40d. These days, I think you can already get War Elephants via the new training scheme, given the right setup. And obviously biome (or Elf trade importation).