Not during the same impulse. The instant the HQ is activated, you pick which units will move that impulse, then complete the moves.
You can; however, move the HQ into a position so that it'll activate a different set of units the next time it is activated.
Also, note that you can move non-HQ units in such a way so that they are activated my multiple HQ's during the turn. So a unit activated under one HQ moves into the activation range of another. When that HQ is active, the unit that moved previously will be able to move again.
Got it! Thanks.