Is It Okay To Go For A Win On Time In Drawn Position?

Recently, I played a game to the point of which neither of us could win, the position was a clear draw, but I had a couple minute in time compared to his mere <30 seconds (there was no increment).

He was offering me a draw, but I declined and played a few more moves, hoping he would make an incorrect move. He didn't, so I sent a draw offer and he gladly accepted. 

Did I do the noble thing, or should I have played different moves and taken the win on time despite the position being a draw? 

I don't think that's correct. If it were a draw due to insufficient material, yes, the game would end a draw, but this was positionally drawn. I could have played the incorrect moves and drained his time rather than have a draw by repetition or, in this case, an agreed upon draw. 

If I had mating force on the board, I would have cheerfully run his clock out.  Let's say the Cowboys are playing the Redskins in football, and they're ahead 21-14, but with 30 seconds left in the game, Washington gets a first down on its 20.  Can you imagine what would happen if someone in the Cowboys' defensive huddle said "Well, the gentlemanly thing to do here is to stand aside and let them score a TD so that nobody goes home a loser."?   

Depends on the position and the clock.

Something like this you can still play Bxg6 and Bc4 so they can't do 100% premoves, so you can use that to milk the clock for some extra seconds.

In a position like the one above, if you have a few minutes and they only have a few seconds then IMO you were the better player (because they needed a lot more time to understand what was going on), so a win is not an incorrect outcome.

However trying to win a position like the one below is just ban maners IMO.