If it was NiCd then a deplete recharge might be a good thing, but a lead acid, such as an AGM doesn't like it.
It is a good idea to 'exercise' the battery regularly but only in taking it down to about 12.2 to 12.4 volts before a proper recharge.
The AGM has a low internal discharge rate so it can survive a few months without a maintenance charge. Letting one sit, though, is not the optimum for longest life. You should use a battery maintainer that will keep a proper float voltage and provide some desulfation technique during storage.