Can I plug a Netgear Nighthawk Pro XR500 directly into my console?

It's more of the other way round, as the xr500 acts as router (and AP), while the console is the client connecting through it to get internet access - but, yes. You obviously can connect your console directly via ethernet to one of the 4 ethernet ports of your xr500 - this should always be faster and more reliable than using a wireless connection.