5.42 COMBAT HQS
Combat HQs forego the option to mobilize. They remain active through the Combat Phase to provide Airpower and Combat Support to any units within their command range.
5.3 COMMAND RANGE
Activated HQs have a Command Range(in hexes) equal to their Command Value(CV). Command Range cannot be traced through impassable hexes/hexsides or enemy controlled hexes
My conclusion is that Command Range is obstructed, thus the units don't get support. Airstrike use Air Range, which is a different matter:
5.5 HQ AIRPOWER
During combat, each active HQ can conduct one Airstrike into one Active Battle within Air Range (equal to the HQs Command Range, but unaffected by terrain or hex control).
I hope this helps.