I don't know each airline's policy but I have heard Bob Crandall comment on many interviews on TV shows that 3-5% of the capacity is allocated for award travel at AA. Unless they adjust that percentage downwards (which is possible) it should not affect probability of award seat by too much. It will be slightly lower because all fare classes are nested which means if the flight gets completely full before award travel is booked then an award ticket cannot be issued thereby yeild less than 3-5% resevered capacity for award travel.

Also, I think award travel once booked has all the same privileges as a regular paying passenger.