Will iPhone 5 power on without a battery

Hi. I just bought 2 iPhones, one is a 5 and the other is a 5c. The batterys are dead and the sreens are cracked on both.

Their in pretty bad shape.

The 5 powers on when connected to a pc though itunes. It throws an error when I try to restore it (error 21) which seems to be a battery related error.

I'm willing to buy a new battery and screen, but first I want to test if the battery is the problem, if I plug the phone into my pc without a battery will I break the phone?

Even if it gives a different error that could be an indicator that the battery is knackered and is causing the problem.