It depends upon how you define an HQ and how you define the personnel assigned to it. In the army, everyone is a basic infantryman first. Having been in an HQ, if we went to the field, we still carried a rifle or sidearm - whether supply, mechanic, chaplain assistant, radio operator, truck driver. For designers, representing tail to teeth issues is not a simple factor. If anything HQ and support elements are dramatically under-represented in most TOAW scenarios.
Consider if a division has a TO&E for 10,000 rifles - 3 regiments x 3 battalions x 3 companies x 3 platoons x 3 squads x 10 men each, provides a base of 2430 riflemen. Add in all of the support/heavy weapons, and we're still far, far short of a division's real strength. A division is not going to roll over just because its assigned infantrymen are dead/captured, but its typists and clerks will be filling in to the extent that they can in extreme situations. That's not to say that these components have the same stats as a rifle squad -- but not every situation where they are needed as a unit will involve taking on a Tank Corps. It could be partisans, a mauled rifle brigade which still has 1 horse team assigned, or a recon battalion.
Between the Winter of 1941 where chefs, cooks, mechanics, quartermasters were used to provide local fire brigades for the Germans, to Operation Bagration and the Destruction of AGC, a variety of other pockets, a few airborne operations, there were plenty of occasions where HQ components were thrown into the gap or became the only local opposition. Eisenhower complained about and asked for more infantrymen only to be told by Marshall to start reassigning clerks, etc. HQ's have duty rosters for guard details, also serve as temporary posts for personnel transiting to/from front line units for medical/leave/reassignment - have military police attachments, etc. and so forth.
Certainly, while the senior officers of a corps won't be meeting the Tank Corps head on... we're talking about a few men.
All in all though, it depends upon the scenario, map size, unit density, level of engagement, how partisans and other rear area threats are represented, supply settings, etc.
A scenario is not simply a map, an OOB and a TO&E thrown together - but one could do that and come pretty close to having something halfway worthwhile or even better - for potentially anything ranging from Alexander the Great to modern warfare.
TOAW does have some issues, but it has evolved over 15 years and there are efforts to evolve it further. Everyone has different expectations of what it should be able to do or handle different things -- part of that relates to the game engine itself and other parts relate to scenario design "by anyone who cares to design."