I don't want to advertise cheating or give any info about cheating, but a "good" cheater can also cheat in bullet and may be even go more undetected if they were to mix moves well.
Note: I have not cheated myself, but I can definitely see a way it can be done. I'm not sure if it would be good of me to describe the process of course... Just think what input you can have and what output you can get if you were to do this programmatically and you can very well imagine if it's possible, there are also existing tools for that. You don't have to open a chess engine in another window and manually do the movements, if you know how to script.
In bullet, I think may be, you could technically even use something to do "anti blundering", meaning you will blunder a lot less, because engine will just check whether it would be an obvious blunder, and block your move. May be you just allow few blunders, and I imagine it would be undetected. Sorry, again for brain storming about that. It is fascinating topic though. Engine could be running on a lower depth and it could be more sort of positional engine that does not do magical engine moves, but is trained on human players and using neural network mostly. Maybe it will just help you do theory openings. And you won't be able to charge anyone for cheating for following opening theory.