Time to necrobump this baby because the answer to the OP's query is YES!!!
Xbox Live on OG Xbox does lives again!
Insignia Live is now live in "closed" beta form, but they are currently still sending out invites. If you have a modded system, pretty easy to set it up. Unmodded you have options as well!
Request an invite here and get started:
https://insignia.live/
Tutorial for modded consoles
Tutorial for stock consoles