My landlord is threatening to counterclaim for more than my deposit, should I still file?

That threat is real, not just a scare tactic, a landlord can file his own claim against you up to whatever limit applies to his side of the case. The question isn't whether he's allowed to, it's whether he'd actually win.

Take an honest look at what he could realistically document before you decide to move forward. If there's genuine, provable damage beyond your deposit, say $4,000 of it against a $2,000 deposit, filing your claim can hand him an opening to come after you for the difference. That's not a reason to walk away from a legitimate claim, but it is a reason to know exactly what he could plausibly document before you start.