Well the book said that they actually have a dedicated (well a few, redundancy, you know?) Astrophage powered DC generators. They turn miniscule amounts of astrophage into electric power for the ship to run its systems. There's also battery backups.

Minor spoiler for something that had more detail in the book, but also happened in the movie (towards the end, with an explosion).

Tap for spoiler

The original Science Officers blew up in both the book and movie, because in the book they were experimenting with a corner case of the generator that could cause it to overheat and explode. However they thought they were doing the experiment with a nanogram of astrophage, but they ended up doing it with a milligram, which is 1,000,000 times the energy density. So instead of the generator simply overheating and maybe menting, it blew up the entire building, even atomizing the metal and everything.

The spin drives also don't generate electricity for thrust, so there isn't really any way to "siphon" it off.

However I am inclined to believe your train of thought, if nothing else maybe they just didn't have a way to use the DC generator while fuel wasn't flowing for the engines (although that seems like a design flaw, but the ship was definitely rushed)