Also depends on which aspects of being a "monster" you care about. I've played as tentacle blobs with far better morals than the typical shitstain psychopath human protagonists in many non-con games, to say nothing of outright torture sims.
Plenty of furry kitchen sink games like CoC and TiTS let you transform into anthropomorphic creatures, sometimes rather elaborate chimeras too. But socially you'll still be a (weird porn-logic) person and most partners will be too.
Likewise in a game like Non Monstrum you do weird non-human things even during sex and are explicitly called a monster in-universe, but it's mostly lesbian romance not an orc rape horde.
I've seen a few "orcs/goblins vs elves" and "defeat adventurers to fuck them" games too. Pabisshu and JSK Studio have made a fair number of Flash-based ones with combat minigames.
TL;DR: yes.