Kind of, yeah. New York City having mutant animals lurking around every corner would take away the uniqueness of being a mutant turtle.
Think of it this way: Would the Powerpuff Girls still seem as cool if every kid in Townsville had Chemical X superpowers? Would the Power Rangers still seem cool if every teenager in Angel Grove were part of a super sentai team? Would Inspector Gadget be anything special if every detective on the force were a cyborg?
It would depend. If said characters' appearances were spread across several episodes and the writers didn't rely too much on them and they actually made a significant contribution to the plot(s), then no, I wouldn't object. However, if said characters' only existed on the show to justify their presence as over priced plastic figurines on the toy store shelves and the episodes began to adhere to the formula of "Turtles meet the-fill-in-the-blank-mutant animal freak of the week", then yes, I would object.