Yes, IanL, there is green radio status in the Damage panel whether or not the company commander is atop the tank. If the commander is off the tank, the C2 radio icon on both the tank and the commander disappear. The Special Equipment panel never shows a radio for either unit, whether or not the commander is riding. The tank's Special Equipment panel does show binocs, so I'd assume there'd be a radio icon, too, if the tank had one.
Curiouser and curiouser. When my Mortar Battery HQ — which also doesn't have a radio — climbs aboard one of the tanks, the same thing happens as with the infantry company commander. What's also strange is the lower echelon 1st Mortar Platoon HQ does have a radio while his immediate superior doesn't.
Methinks this is not the way it's supposed to work.