Accepted answer: no
My friend and I started playing BL2 in a LAN centre this evening for a bit of fun.
We got some way into it, then his machine restarted, which meant his save game was lost (as the LAN centre machines wipe stuff off when people log out).
I quickly zipped my save folder, emailed it to him… he loaded it up, it loaded up… he could see my character,and we could find each other's game on the network, but were unable to get in… it did the 30 second timeout countdown, then that was it.
So, my question is twofold:
1) Is it possible to play the same character from the same save file together on two machines?
2) If, in future, we return to the LAN centre and copy our save files, will we be able to play them online, or does moving save files around automatically make them offline only? (This appeared to be what had happened, as further tinkering seemed to indicate that this transferred file could not participate in any kind of online/LAN game we tried to set up, even with a newly rolled character.)
Maybe this is important - this game was not using Steam in any (visible) way. We certainly weren't logged into Steam.