The FAA (Air force) can boast 632 aircraft
No. Adding up the aircraft in the table they provide, you come to a figure of 270. Out of those, 19 Mirages III and V are "in storage", 1 Boeing 707 is "retired", 13 IAI Daggers are "in storage", half the 8 C130s are "operative", and the 7 Su-29 (eh?) are "in storage", for a figure of 236.
18 of those are C182s, plus quite a few Fokker Friendships and VIP runabouts; 195. Then there are 12 Saab 340s and Twotters and 72 operational trainers, leaving 110. 32 of those are helis.