"Time to see what my latency on the server is."

[Eye_Gore]

I imagine you can. Just do what Secrets said. You PS4 goes off your internet so I dont see why it would be different. Unless PSN does things drastically differently.

There's no cmd prompt on a PS4 so you can't ping from there. I'm not sure if speedtest would work on the PS4, if it does you could atleast ping a server in the city where the data center is to give a rough idea. Though if the PS4 routes through the PSN before the data center there will be more latency than a direct connection. I'm not sure of the connection routing.
Also to give a rough idea is just ping it from a PC in your house.