Might be tricky. I think ultimarc sells an adapter for the xbox to allow you to hook up an arcade monitor. But I thought it only supports standard resolution. So you'd have to switch your monitor from medium res to standard. If your monitor is like my Nanao in my Daytona you have to move the connector from medium to standard on the monitor's pcb. Not hard to do but it isn't as easy as throwing a switch.
Sadly, my Daytona USA was lacking boards..... but I can't complain as APFelon hooked me up nicely with the main cabinet/monitor.... (thanks again, APFelon!)..... so it wasn't an issue for me to install a semi-permanent console in there.
Also the pots for the Daytona are 5k pots. When I put my Dreamcast in my Daytona cab I had to replace those pots with the ones from the Dreamcast's steering wheel as they weren't 5k pots. Fortunately they fit without too much work. Again, you'd need to work something out unless your xbox steering wheel uses 5k pots. Maybe if the xbox wheel uses a 50k pot you can add a 45k resistor in there to make it compatible with the xbox wheel? Not sure how'd you work out the "switch" tho......
You might poke around the console forum here too.
Good luck!