I think I know the answer to this from my googling, but i dont want to believe it to be true.

is there any way to play the backed up versions of my games on xbox live with a mod chip?

this pertains to xbox 360s

You cant. Ever. Its happened before, but youll only be able to probably just played custom, friends only, unranked games, just for the fun. If you wanna use it to rank up fast and be a big bitch about it cause you suck, they kick you off, ban your 360s serial code or some shit from it, and your IP. So yeah unless you want 2 360s which would be the best answer, have fun.

AFAIK you will never be able to play burnt games on Xbox Live.

But while on the subject, for offline play:

I don't know if you can do it with the 360 (I can't see why not, though), but on my Xbox I had one of the good Xecuter chips installed so as that when you hit the button it'd boot up without the chip on and you could play on Live completely undetected, then when you wanted to play burnt games you could hold the power button down for 2-3 seconds until the ring went orange instead of green and the chip would be activated until you turned it off again.

Because the 360 doesn't have a hold-down power button like the original Xbox, a flip switch somewhere on the back of the case would do it just as well. Maybe even a big red military toggle switch for shits & giggles.

You can also get your 360 flashed, but as far as I know that will mean you can never go on Live, ever, as it's a full time mod.

you can go on live with custom firmware and backup discs as I have done for the past 2 years now.

its a risk you take though, if they develop a new way to check for the firmware then you get a banned console for your efforts.

Is live worth it to you?

the xbox would suck without live, so yes it makes the console.

and if I did get banned I would simply sell the console and buy another as a replacement