Maybe somewhat, although Harrenhal doesn’t seem to have been a major destabilizing force since the reign of Maekar I.
That second question is a bit tricky. Under normal inheritance rules, you’re quite right. But Harrenhal is special and hasn’t obeyed normal inheritance rules repeatedly over the last three hundred years. So it probably depends on whether the Iron Throne is exerting control (as they are with the Holy Hundred) or whether the locals are in charge.