Operating the Touch with a local server should work fine with a dialup connection or with no internet connection at all. The initial setup may be tricky, though. It will insist on registering itself at mysqueezebox.com. I've never tried it, but I assume that would work fine over dialup. You can also skip this step in the setup by swiping the touchscreen from left to right when it asks you for an email address.
It might also try to update its firmware, which could be a chore at 56k. Except during setup, the way firmware is normally updated is that the server downloads any new updates and then pushes them to the player. If that happens (your server would need access to the internet) and the firmware downloads go OK (although they'll take a long time), then the Touch will have no problem updating itself when necessary.