Does Account Abstraction support "Burner Accounts"?

Yes, Account Abstraction can be used to implement Burner Accounts.

There is a very good open source implementation here

For a brief description:

The Starknet Burner is a Key Manager, i.e. a library that you add to your application and helps users to manage keys that are not their regular signing keys. The way it works depends on the type of keys. For now, the burner manages session keys, i.e. keys that work with an account that has a plugin setup and have been authorized by the signer offline.