This mostly happens with players below 1300s...When they make mistake they spam draw offers.... happens to me a LOT
I would NEVER do that. Ever. That's beyond the line of Chess etiquette. And remember, I am only a '900' on here (about an 1100 in real life).
It happens in OTB tournaments all the time when you're playing noobs. You see the same scenario all the time...some sub-1200 rated guy is down ridiculous amounts of material, is about to get mated, and offers a draw.
It's happened to me and I make it a point not to go over the game with them afterwards. Offering a draw like this is just as bad as making people rated 500 points higher than you play out to checkmate instead of just resigning.