If I replace the battery in an iPhone 5 will it come back on automatically?

Currently I have 65-70 iPhone 5's or 5c's deployed within my organization. I have one iPhone 5 with a bad flex cable; which means the power button doesn't work. The only reason why I haven't replaced this device yet is because the unit will turn itself back on once it begins charging.

Recently the battery life on this device has become suspect. I was wondering if I replace the battery completely, does the device still turn back on once it's charging?

Has anyone ever gone through this? If so, please provide specific examples.

I'm confused, why do you care if its on when charging? That doesn't matter.

Since the flex cable is bad I can't power the device on manually; the power button does not function. The only time the device powers on is when it is charging. So I need the device to power on while it's charging otherwise it will become completely inoperable.