I think it all depends on the particular animal and the particular situation. The less the stage time for the animal the better. For instance (SPOILER...I guess it is still considered one) -- the cat in the
Lieutenant of Inishmore worked great.
...but there can be the alternative...
My vocal coach in college, who used to perform with a professional opera company in NY, told me this story as his raison d'être for not using animals in any live shows:
During one opera he was performing in the director had an idea to use two poodles in the show's opening. The plan was that as the curtain rose, the poodles would run in from opposite sides of the stage, cross paths, and then continue into the wings. However..it didn't quite turn out that way...
The two poodles entered, met at center stage...and then...well...decided to start conceiving some future poodles there on center stage -- as the curtain rose on Act One. I can only imagine what the audience reaction was (of course someone probably thought that there was some hidden aesthetic meaning behind it).
The moral of the story is to either not use animals at all -- or make sure they are not of opposite sexes.
"You pile up enough tomorrows, and you'll find you are left with nothing but a lot of empty yesterdays. I don't know about you, but I'd like to make today worth remembering." --Harold Hill from The Music Man