The real-world documents are linked on a pinned post on the Torquesim discord. You can also find it by googling "c525 ptm". There are 2 volumes (V1 and V2), one with procedures and one with system descriptions.
I recommend reading through the expanded checklists at least once, because it helped me to understand some seemingly unnecessary steps in the checklists (e.g. "Throttles ... as required" on descent.
As far as I understand it, that's basically the point of the GPU. The batteries in the CJ are pretty small, so if you're sitting on the ground for some time with BAT / avionics on, you might not have the > 24V required for the engine start anymore.
Obviously you have to turn it back on before engine start. At night, I don't turn it off at all, because otherwise I'd be sitting in a dark cockpit.
This is a CJ1+ (different engines and Proline 21 avionics), but it's the closest I could find that shows the engine start from within the cockpit (time: 28:16).
Notice the PFDs are off, so the BAT switch is in EMER. You can see CM1 (left seat) turn the switch to BAT (you can hear the fans powering up) at 28:28, right before the "Before Start" check list.