I would like to be able to use and make mods for Fallout New Vegas for the Xbox 360, but so far, the only way you can get mods for consoles are with certain hardware, which has limitations.

I'd love to be able to use a GECK on the Xbox 360, but would it be possible?

No. The GECK is a windows program, the 360 does not run windows programs. Also, user made content for consoles is not something that will be permitted.

Discussion of modifying the 360 will get you a PM from a moderator you don't want.