For the most part yes, any PSU can support any motherboard, however, there are exceptions especially if you include some of the older OEM systems, Dells used to use custom connectors on their PSUs and motherboards that made them incompatible with regular ATX units.
But for the most part if you have an ATX 2.x PSU and an ATX 2.x motherboard they will work together. There are some strange motherboards that need 2 8 pin EPS 12V connectors but if you are getting one of them you will be getting a high powered PSU anyway which will likely have a 4+4 and an 8 pin.