No. Only AF 9 have unlimited air formations. AF8 and less only add the best HQ’s radius to the number of formations you can operate (on missions other than search or training, and not resting).ORIGINAL: Sardaukar
So, basically, to answer original question, Air HQ bumps size of air base in PH over 9 and immune to administrative stacking limit.
Check Clark Field at start. AF8 + an air HQ, yet it doesn’t have unlimited administrative formations.
EDIT: and by the way, Command HQ also help. Well, not « also » as much than « in place of an air HQ » as Clark has a formation limit of 17 (AF8 + USAFFE range 9) instead of 13 (AF8 + Far East USAAF range 5).