I believe this quote answers your Question.
As per Hermione
Hermione: "It’s impossible to make good food out of nothing! You can Summon it if you know where it is, you can transform it, you can increase the quantity if you’ve already got some..."
For instance the spells Molly Weasley uses to cook with would surely involve the preparing of Animals and then the cooking of them into food.
It appears I was misled by the question body and did not answer the title question.
As I see it a Transfiguration would last through an animals death as it is not a part of the animals magic it is to do with the caster. For instance you could transfigure a Cup into a Gerbil (inanimate to animate - Cornelius Fudge does so in front of the Prime Minister). When you transfigured you change the structure of the object/being (not limited to inanimate) into the new object. As far as the magic itself goes it is the most scientific of the magic that we see by which I mean it requires the most precise actions to achieve a desired result.
"When Transfiguring, it is important to make firm and decisive wand movements. Do not wiggle or twirl your wand unnecessarily, or the Transfiguration will certainly be unsuccessful."
—Emeric Switch, A Beginner's Guide to Transfiguration.(pottermore)
-The following has no found canon quotes as of the moment so please do not take it as complete truth refer to the comments for a discussion with the esteemed HP answerer @alexwlchan.
It's worth noting that Transfiguration is not permanent which means you couldn't transfigure a piano into a cow and then cook and eat the cow as at some point it would turn back into a piano. That would be bad.