I can't see anyone objecting to a fish or something. As for cats and dogs... my guess is probably not, either because other people would object, they would be bothersome, or the lease would not allow for it. So it's possible, but unlikely.
Thanks for the reply. Great idea to get like minded people together. We hope you plan to share the stories and results from the house. Will make interesting reading if all house mates end up making it big.