I did the simulation 10 times. Nine times we stayed at pick 11 (which means a team with a worse record than us won the lottery, so any changes in order didn't affect us) and once we moved DOWN a slot, because Buffalo won a spot at the top of the lottery.
All finishing in the bottom 11 does is give us a chance, albeit very small, of winning the lottery and getting the #1 pick. But we do also have a chance of moving down, which is probably larger than our chance of moving up. To move up, we'd have to get a winning number ourselves; but if ANY of the teams in the lottery with a better record than us gets selected and we don't, then we move down in the draft order.