The accessories should not have any affect on how it starts. Only on the load the alternator has to put out to keep up...
(Wow, I said "keep up" and "put out" in the same sentence and didn't refer to a Kardashian...) LOL!
The purpose of the battery is to store charge to start the car. The alternator takes over once the engine is running and supplies all the power to run the engine and accessories and put the charge back into the battery that was used to start it.