With Avis Preferred, even if you have to go to the desk, there is usually a 'fast lane' which jumps the queue or is at least a shorter one. It's free so there's no reason not to have it.

If the car upgrade is essential, then I would talk to BA Holidays to try to book in advance.
However, my experience is that I have often been offered a choice of cars including higher groups for no extra payment on arrival. Not sure if the Preferred card helps with that.