Yes, the thing giving it power is the amplifier and the electrical circuit it’s plugged into. And unless the guitar itself is wireless, the guitar is plugged into the amp…

It’s entirely possible to plug a messed up guitar into a perfectly good amplifier, and then the next thing you know you’ve got a shorted amplifier. It’s called a cascading failure. No it’s not all that common, but it can and does happen.

Is it so much of a stretch of the imagination to be better safe than sorry, not take any chances, and treat the equipment with a little respect and at least inspect the internals before plugging it in?