Can solar controllers and smart chargers be used simultaneously?

International companies like CTEK, Sterling Power, Enerdrive, RedArc, Mastervolt manufacture chargers that allow solar and either DC charging from an alternator or AC charging from mains supply. The reality is if there was no current being discharged regardless of the charging source (solar or AC/DC) if a battery is floating at 13.6v that's because it's almost fully charged and both devices will within minutes both settle at 13.6v to float charge or maintenance charge the battery. At night the solar controller will be off and the mains charger will finish charging the battery. By the second day the solar controller will turn on as the sun rises, voltage will quickly rise to its pre-set bulk voltage before dropping back to float voltage for the rest of the day. While the solar boosts voltage to its bulk amount the secondary charger depending on the charge algorithm the unit may stop supplying current as it's not in control of the rising voltage to bulk. (the current is what's pushing voltage up, so it regulates voltage at 13.6v but cuts current) But once voltage comes down again and additional current is required it will settle back at 13.6v or float voltage.