I actually quite like this idea.. It doesn't really have the 'It's like stealing,' drawback that just resurrecting another's pets from their graveyard would have; the player's acknowledged that they're letting their Creatu go.
I s'pose it would probably end up full of mostly natural pets, and there would be no chance of finding awesome names, but it could still be of use to people. If you had a name you really wanted to use or claim but were out of hatches, your graveyard searches would provide an excellent opportunity to get unnamed pets. And maybe, by very slim chance I imagine, you could find rare, valuable Creatu. Sometimes people do forest and give away pets like that, for one reason or another.
I do think it should be just five searches a day though, since you don't seem to have mentioned that.. Just like the Atqueen Forest, except they're dead. x3