When an HQ is overloaded, there is always a rating penality, increasing with the overload. So rule of thumb, it's better never to overload when possible. But sometimes other considerations may come in play of course, so better to keep an open mind on things.
That said, when you realize the importance and incredible quantity of ratings die rolls for every unit at every turn, you understand how important they are. My own perception is they have much more impact than air support.
"The closer you get to the meaning, the sooner you'll know that you're dreamin'" -Dio