That’s a very complex question. For example, if you turn off an iPhone, it’s still on, just in a low power state. If you turn off a mac, same thing.

Depending on what kind of software they have, they most likely could take advantage of that type of thing to allow for communication with your system when it is “off, but that would probably require there to already be something on your system.

I can’t know how advanced or complex their software is, nor know if they have back doors built in to generally distributed OSes or hardware.

So, in summary, it is possible, as long as power is available to a system, for that system to be attacked in some way. If you have a desktop computer, and you’re super paranoid, you could unplug it.