The general thinking is that going in the drops gives you an aero benefit (which is basically meaningless on a climb) at the expense of being able to take deeper breaths (which is critically important when climbing). But as has been noted here, the higher gear ratio and the opportunity to engage your low back in the climbing action might mean that the story is different for fixed gears.
But I kinda doubt it.
For me, nothing makes as big a difference when climbing as state of mind. If you feel like joe racer in the drops, you very well might climb better.
Just do whatever is most fun and enjoy it.
