There are different ways of having a giant AHU and 20 VAVs. You could have one giant cooling compressor for the AHU, a cold deck in the giant AHU or, a more modern or efficient system may have a common warm water loop circulating between the 20 VAVs, and each VAV has its own heat pump compressor for local zoned (modulating demand response) heat or cooling.
You suggest electric heating as if it may be resistance type units. Could be set up as electric resistance backup or second stage heat, but if its primary electric heat, I would be looking to see it that's a problem. Modern system could have electric heat pumps at each VAV, with an air to water HX to the common shared warm water loop. With central plant supplemental heating and cooling equipment sitting on the warm water loop as necessary.
Supplemental primary central heat you would want gas (methane). Otherwise the VAV mounted heat pumps could cool and dump the heat where it is needed, or to a central chiller.
Your question pertains to the equipment topology and if the auto control system has a mode where everything runs (at full) at the same time. It's not clear what topology you could have.