The actual vegan response: http://ethicalvegan.net/read/will-animals-go-extinct-if-the-...
It comes down to "Stop thinking about extinctions when the factory ranching system is a bunch of concentration camps."; that is, they never deny that their policies would lead to extinctions, they just insist that ending the cruelty is a more important way to frame the debate.
Subsidiary question: Is it really extinction if the gene line is preserved, but never allowed to ramify into an actual organism?
It wouldn't take many generations to breed them to be friendly and docile rather than fast growers. Maybe a few more to better adapt them for housebreaking or litter training.
They would also continue to be used in medical research and truffle hunting, of course.