[Imp]

The HQ is the only none fighting unit in the game it represents your link up the chain of command to units off map. Think of it as the guy in the command tent or the Batman sent forward from it to ensure orders are carried out.
Its loss therefore effects off map unit contact but the major effect is morale plummets because your on your own now the chain of command is gone.

Like all things in this game the AI gets no special treatment kill the HQ as quickly as possible if you find him.
Takes a couple of turns to take full effect but the morale collapse & rally problems are easily noticeable its a big hit.
Its the beginning of the end morale will plummet as now combat is far easier so the remaining forces are just witnessing getting wiped out.