I think it depends on whether you're talking about getting more than one Tivo.
With multiple Tivos, yes, they can all be connected to your home network (wired or wireless) and can share content. So a show recorded on the Den's Tivo can be sent to the bedroom's Tivo for viewing. My parents actually have three networked Tivos (setup by me), and they regularly send content from one to the other for viewing on different TV's. It works pretty well (Wireless G), and they like the setup. And yes, I routinely remind them that most normal people don't need three Tivos, one of which is even a dual-tuner Tivo.
But even with just a single Tivo, it's still possible to send the content elsewhere.
A simple coax/RCA splitter could send the signal from the Den to the bedroom. But as you already know, yes, it'd just be a clone of what's on in the Den. And unless you got an RF remote or the bedroom has LOS to the den, you're not going to be able to use the remote to control playback. Perhaps not very useful.
However, Tivo does provide a free Windows application that allows you to copy the shows recorded on a networked Tivo to a PC. So if you had some sort of media PC in the bedroom, you could use that software to view recorded shows from the Tivo. The process is independent of what the Tivo is doing, so users in the Den wouldn't be interrupted. The catch is that it isn't (or didn't used to be - it's been a year or so since I last tinkered with it) a streaming process. You'd initiate the transfer and it would take 30-40 minutes to copy a one-hour show to the PC. *Then* you could watch it. This was via 802.11g between Tivo & router, wired from router to PC. Would likely be faster with hard-wired connections. So it did work, but it would require a little preemptive planning.
Good luck!
