Which PSU specifically? 650W doesn't tell us much at all unfortunately. Make/Model?
I would say the GPU is more than capable for 1080p, yes.
As far as performance goes, it' sits somewhere between a 1050TI and a 1060..... while consuming more power, obviously.
Considering a 1050TI is a 60FPS Medium-High @ 1080p, and a 1060 is easily a 60FPS High-Ultra, 1080p..... the 280X should still have some solid life left in it.
I would suggest it's probably more in the 60FPS @ Medium-High 1080p...... with some titles needing to be turned down closer to Medium.