Yes to both questions.
* Except for very large transactions where you might hit a NFC bandwidth limit, but extremely rare.
Discussion
Would you run into a limit with a Tapsigner? It’s just like a blind signer, right?
Yeah, it's a blind hardware signer. With Nunchuk, it basically uses the Tapsigner as a key so that the Tapsigner is called whenever you tap the button to sign your transaction. And Nunchuk manages backup creation as well, so that if you lose or destroy your Tapsigner, you'll be able to restore the backup to a software key so you can access your funds. I don't believe there's any fund limit imposed by Tapsigner. It should be able to sign transactions regardless of the size. Personally, I love it and it's been a great experience when paired with Nunchuk.