It would not change my answer. I think that table draws should always be random, but in the real world of OPs game, the charity room where I play, home games and other situations, what we think of as standard poker rules and practices don't always apply.

We need to navigate those situations the best way we can, and sometimes the right decision might be to not play. If there was a casino close to where I live (the nearest is 102 miles) maybe I wouldn't be playing at my local charity room.