Will HomeKit remote access still work if I add a VPN to my Apple TV?
Your VPN connection isn't really a factor since all the of the synchronization is done via iCloud.

To simplify this a bit, consider that to remotely control your HomeKit (via the HomeKit hub), your devices must be signed into iCloud with your AppleID.  When you're away from home, you're on a different network and control your HomeKit devices.

A VPN is nothing more than a secure way of connecting a computer on one network to another so that it you're actually on that network (i.e. you're in Paris, France, but you VPN into a network in New York).

So, whether you're on a remote network or on a remote network but connected to a VPN, so long as you can sync with iCloud, you can control HomeKit devices.