Yep. You can of course backup the DB on the Kobo itself (as long as it hasn't done a full factory reset, it'll still be there). If it's still there, then you don't need SQLite on the computer you connect it to.
Also, if you have a backup of the SQLite DB on a USB stick or memory card, you still shouldn't need a computer with SQLite on it to copy that back onto the device (if the backup on the Kobo itself for some reason has gone or didn't work).
Backup books on a micro-SD card is also key in this kind of "away from home", recovery situation.
I have a backup of my Glo's DB from just after was registered, on the Glo, on my netbook, and on my file server at home (which I can get a copy of, from any internet connected computer). I suspect you might even be able to create a plugin for Calibre to backup the SQLite DB both on the Kobo and copied down to your pc, as part of what it does (if it doesn't already).
I think I already also said before, you could probably get the "registered" SQLite DB into the recovery image, with a little work, so that a full factory reset, would skip the registration step, which would bypass most of this issue of getting going again. I might just try that at some point.