It is really hard to know without an idea of what the set-points are for the auto charger. But from your past experience, it looks unlikely that the auto function is enough to get it charged back up in any quick fashion.
My auto charger is all but worthless. As soon as it gets up to 14.4 it immediately drops to 13.6 instead of holding at the higher charging Voltage for the necessary time.
There is a bunch of info out there on charging profiles for deep cycle batteries - you should see if you can find out the manufacturer of yours to see what they recommend.
