I know airliners need to divert air from the air circulation system in order to start the engines. I was stuck on an aircraft that couldn't start until they fixed the system.
However, I've been reading enough about how Teslas have been able to sit in the sun or freezing weather and still operate heating or cooling while they charge. They have to be powered on during charging to control all that stuff anyways, including possibly cooling the batteries while they charge. However, the primary mission of the cooling system will be to cool down the battery on a hot day, so it might divert some of that. That the battery is actively cooled is probably one reason why the batteries might last so long compared to consumer electronics that don't typically have any battery cooling.
The big thing seems to be whether or not certain eco modes are turned on to reduce the use of battery power for heating or cooling. However, I've looked around and a Nissan Leaf, Chevy Bolt, BMW i3, Mustang Mach E, etc. usually can charge and blow A/C at the same time. However, sometimes the user has to play around with the settings to get it to work since many are designed to use as little electricity as possible and the general idea is that most users aren't going to be charging and staying in the vehicle.
It's kind of interesting too as some of these vehicles use heat pumps for more efficiency, where the heat from the active systems can be used for heating the passenger compartment. But it's a bit like a traditional water cooled vehicle where the coolant provides the heat through the heater core.