About 5 problems I see with this
1) Getting to a BASH prompt - while not difficult; would be interesting to do if needed.
2) Connecting - You would need a Tivo(Turbo)/Net card and then I'm not sure if it would work. PPP(Serial) might also be an option
3) Speed - I think the TiVo runs on a 266 mhz box; add that in with the time to index the results; not really sure how long it would take.
4) OS - While it does run Linux; it runs a very very scaled down version; with only the minimum drivers; not sure if that would hurt.
5) App conflict - Again, not sure; TiVO is a very unique thing.
You may want to ask your question in the Underground forms @
TiVo Community
Sorry to be the bearer of bad news; but if you could get it to work I would be in AWE!