If we offer a draw, that has the most likely connotation of being a sign of weakness; therefore Mr. PawnRiot will refuse gladly and play on.
Because Mr. Riot is most likely the stronger of the two, between the forums and himself, he will offer a draw when he sees fit. If it is Mr. Riot who should initiate the draw sequence, then it might even be considered slightly rude to offer a draw.
Certainly it's not the case. It's never rude to offer a draw in an even position, as long as you don't do it repeatedly.
We have a forced draw, and this is probably our best line. Whether he accepts it or not doesn't matter, it's forced (if we decide to play it). It would be a little like refusing to accept a checkmate.