Can my IPhone be off when I am doing the manual back up? Or will the backup pause once it is off?

Depends on what exactly you mean by “off”

The screen being off, does not actually turn off the device, and the backup would still continue.

If you completely shutdown the iPhone, then there’s no activity whatsoever, so no backup will happen.

For either an iCloud backup or a computer backup, the phone needs to be powered on.