It depends on the brand and model of the charge controller, and the brand and model of the battery charger, and the voltage they each put out, as well as how smart or dumb, or manual they are.
My little stinking Sears Roebuck 6 amp 12 Volt battery charger that is manual is fully capable of putting out 16.0V. If I run my POS WFCO and the manual charger at the same time, the WFCO puts out nothing... it's forever trying to charge in float mode at 13.4 Volts. The manual charger overshadows it in voltage, so the manual charger does all the work and the WFCO does nothing. Which ever charger has the highest voltage will do most or all of the work in charging.
