The manual has this to say: "The panels contribute to the aerodynamic performance of the car, and also help to keep the engine bay clean. Do not run the car without the panels fitted."
With that aside, they're definitely not structural - you can tell just from the fasteners used. They do, however, support each other, so without the diffuser the main underpanel can flap/bend a good amount.
I wouldn't drive for any extended period or at any speed with them removed, but I too drive to the alignment shop with the diffuser pre-removed.
Leaving the underpanels on seems like a good way to encourage mistakes and/or qballing at a normal shop and extra shop hours billed at a race shop. I'd rather spend the 5 minutes to take them off myself ahead of time and save myself either damage to the car or the .5 hours of billable time.
I could see pulling them in the parking lot, but it seems easier to just leave them in the garage. That way I can double-check the alignment shop's work anyway, and make sure the rear toe joints are aligned correctly relative to each other.
