The is less of an "I need help" question and just some random string of curiosity but is it possible to run some sort of GUI on an OpenWRT router (overVNC or RDP or something like that), for example, the GL-MT300N-V2, GL-AR150, or Linksys EA4500.
I don't think so.
The only 'vnc' software seems to be 'vncrepeater':
I think you need a vncserver.
Well, there is the option of allowing LuCI access from the WAN side (though using a VPN for that world be very much recommended).