Interesting question. I think it's a bit of both. Strays will likely be created by the game creating them and not by "breeding" with existing animals. In that case, neutering is pointless.
However, if existing animals aren't fixed, then they might end up strays. I'm not sure how that works if household pets can spontaneously end up "strays", or if existing strays can even breed. Maybe if the family had a pet and the whole family dies/moves out?
I suppose you can test it by keeping a record of all the strays and fixing them. Then checking periodically to see if any new ones are created by looking in the sim manager menu.
I suppose it's possible the game might not create any new ones if you already have existing ones. This would also mean any time an existing stray dies, a new one would likely be created and you'd then have to fix them.
