IIRC, they don't turn everything off. they turn off the reactor and run the ship's systems off of battery power. against a nearly 0 K thermal backdrop, there's no way an object like this could completely evade detection.

they do actually address this in the show. you can infer from the dialogue that they don't expect to be "invisible"; rather, they are trying to be indistinguishable from space junk.

I do think people are being a bit harsh in this thread. the show isn't perfect, but it's about as hard sci-fi as you can be while still getting renewed each season.