My guess would be they would send a "support" vehicle and not a wrecker-- the same guy that comes for dead battery or the like. Here in SoCal, it's Ford pickups and Toyota Prius-- mostly Prius. I don't think any of us would have difficultly fitting our bikes in the back of a Prius.

I keep my membership current because you have to have a membership to have their auto insurance, which I do. They're not the cheapest, but they are very, very, very good. I've had 3 vehicles totaled out from under me while covered by AAA insurance, and every claim went through absolutely trouble-free.