In any case, yes, you can add a charger.
It would be no different than adding solar, that controller is a battery charger.
IOTA make good inexpensive automatic chargers.
I sometimes run my IOTA 55 amp charger, a 20 amp charger, along with 675 watts of solar, thru a MPPT 60 controller, at the same time to get my large bank up.
As the voltage rises, all of the charging sources automatically cut back, so there is no danger of overcharging.