Hey Jeff
When talking about 2 mics on the same drum and reaching for the wrongly labeled "phase" button. the effect isn't a 180* change... its a polarity flip. (P to P or P to N like you say!) so even the delay time between the 2 mics will remain the same. all it will just change the polarity of the wave form making it interfere differently. and sound differently
Phase has a Time component and is corrected by delay. New digital consoles have the capability to align all the signals in time.
Now how is this going to effect everything in a small room. End of the day its a huge compromise..... as you know if you have 2 mics picking up the same source and one is further away you will get comb filtering. same with hearing sound from FOH speakers, and the bounce back from the back wall of the stage from the monitors, a polarity invert(on monitors) may do the trick to make FOH sound thicker.
It all depends on the situation. room size etc. Its all a case of spotting what is causing the issue and how much you can correct for it.
Delaying the PA to the back line may Reduce a 2nd layer of room reverb (since both signals arriving at the same time or close will decay at the same rate). Clearing up some of the mess and interference.
Whats really gonna cook your noodle is when you think all the backline etc you have mic'ed are all getting picked up by the vocal mics as well and fed back in to the system for another layer of comb filtering too!
We work in an industry where we converge towards perfection but can never quite make it. We just have to do the best for the situation possible!
Like everyone says
Try it! What works in one venue or room may not work in another. This is why the Try it and see is pre programed!
lastly its all down to the ears....Listen and decide what sounds best! Good luck!