I would think it was part of it, since it taps off the line prior to the ballast resistor. So if it still has power there, the coil would have power too.

But regardless, is there a problem in wiring it hot all the time if I seperate it from the wiring to the ballast?

I understand it doesn't need it if the engine isn't turning, just wondering if it causes a problem, like points burning out when you leave the key on, not that this burns out points if you leave it hooked up.
Do voltage regs or the alt have a problem with power applied to the field all the time if they aren't doing anything?