Impatient vs Eager or Motivated
knight:
If it is a unit that is highly competitive to get into, I don't think the hiring board would view a "Thanks for considering my application and I look forward to the results of the board" letter, Thank-you card, or phone call.
I heard of all those things in my unit. Everything I ever heard from the powers-that-be were positive when guys checked-up on their status.
When I was in a hiring capacity at a Part 135 company, I viewed those who showed no follow-up as not very interested.
Good luck...hope it works for you.