It is unclear to me whether Khan's special ability can be executed even if he is currently located in an area with an activation marker.
It seems that flying units (which serve as an example for his special power) can not do this. But in the rules the corresponding sections only mention units and make no reference to heroes.

The section on activiation markers has all the info you need. The part of it on page 21 to be exact. If an action comes from anywhere other than an order card it is not restricted by activation icons unless it specifically says so. So yes, you would be able to use Khan's special ability if he is in an area with an activation icon. That's just how fast his white scars are!

Well, I'm assuming his ability doesnt say anything about it. I dont actually have the game yet and the primarch's powers are not in the rulebook, so I cant check that bit. I'm assuming it doesnt otherwise you wouldn't have needed to post .