I use my monitor all the time, as long as it has an HDMI input and either speakers or ideally a 3.5 out you're fine. I run all my consoles into an HDMI switch, then into a splitter, then into the monitor (and two TVs and a capture card), then the game audio from the monitor into my PC. Works great. Only thing you should be aware of is full vs limited RGB--if your monitor/TV is full RGB you have to manually set the PS4 to full RBG, automatic seems to always go to Limited even when it's wrong.
The PS4 has a system-level overscan compensation, which lets you set it to "no overscan" as well, which is perfect for any sane monitor (or any sane, modern TV really)
Only potential issue I guess is HDCP? I'm not sure if that's a problem with most monitors, but I use a $20 splitter that also strips HDCP (almost all splitters strip HDCP) so it's not a problem. If you want I could test it without the splitter, I would think it would work. You can use the PS4 without HDCP at all too, but then netflix and crap doesn't work. I just leave it on and strip it for the best of both worlds, also out of principle because fuck the MPAA.