I don't see why it wouldn't. Isn't apple's way of handling FaceID in that the secure enclave checks and if it passes then it tells the app in question "Yep the face matches" that way the app doesn't load.
If I recall correctly as well, Android doesn't do it that way which is why the Pixel 4's face unlock was such trash because every app that wanted to use it would have to be updated to look for the face instead of a fingerprint.
I'm hoping that's how it works. I use Enpass for my password manager and already put a suggestion for them to incorporate this, but if it just works with no dev programming that would be so much better.