So, as a full member, could I sign-out the plane for, say, a month, and fly to California and back?
Yes. As a matter of fact, we have members that have done just that (summer trips, honeymoons, etc.). In order to reserve a plane for that long of a time, especially in the summer, the reservation must be made ahead of time. And it’s usually best to clear very long reservations with the club manager first, since he might know of any planned maintenance (to that plane or others) or other issues that might impact a reservation. Additionally, provisional members are limited to single overnight reservations until becoming full members. This rule prevents someone from joining merely to “rent the plane” and fly to Oshkosh for instance.