It's not allowed, and Chess.com has a system, that they have understandably not released the specifics of, to find cheaters, found here. You can use the report abuse link to report your recent opponents, have them reviews.
It's not much of a problem at my level :P but I wouldn't be surprised if there were some cheaters at your level. Good luck!
Is this allowed on chess.com and if not, how do you check if your opponent is using an engine? I'm playing a 2000 in the Canadian championships online right now and I got smashed in both games. Now... normally I don't give a crap and I did make some stupid moves in both games but I don't expect 2000's on here to punish me as hard as he did. Even I have trouble converting winning positions against weaker opposition in long games and on here I don't think most people think or play as well as over the board anyhow.