Will a power supply work if not connected to the motherboard?

Under normal circumstances, all power supplies (including those with an on and off switch) and their fans turn on due to a signal they receive from the motherboard. Therefore, unless your power supply connects to a working motherboard that sends that signal, the power supply will not work.

How to get around having no signal

Users can turn on a power supply without the motherboard by inserting a paperclip into the green and black wire sockets on the 20-24 pin connector. This action allows the user to power individual components rather than the whole machine at once.