I think the answer is probably "yes" but it isn't clear how you're trying to set it all up.
As I read it:
- You have a PC downstairs connected by ethernet to the router.
- You have an Xbox upstairs connected by ethernet to the router.
- You have a second PC (upstairs?/downstairs?) connected wirelessly to the router.
Is there anyway of connecting to the pc [which PC?] via a wired connection in the room [which room - upstairs?/downstairs?] and then using the pc [which PC?] to connect to the wireless network?