Does Account Abstraction work on Mobile?

Yes, because there is not strict coupling of the ECDSA signature implementation accounts must have AA contracts can verify any signature scheme they wish.

This will most likely include native mobile signature schemes at some point leveraging secure elements and Secure Enclave.

Here is a project that has proved out verifying a StarkNet Account using a phone's FaceID feature (notice the elaborate signature field).

Yes, unlike EOA, you can put any frontend you would like on top of your Account Contract. It can be a browser extension, a mobile app or even a desktop app. They will all work the same as the actual transactions are executed via the Account Contract and not the Frontend client.

And for a concrete example of a real-world mobile Wallet App utilizing Account Abstraction, biometric signing and all other mobile goodies on top of Starknet, check out the Braavos - Mobile Wallet: iOS Android

Well, this is what AA is. And as you can see, it has nothing to do with the device where the front-end is running.

AA will run as smoothly as the current EOAs, and should be as transparent as possible to the end user.