Not entirely certain if this is repeatable, but I figure I'll post about it anyway.
My young Trill science officer is now in Borg Space. This occurred after I had invited myself into my fleet with my RA5.
On the Trill, I had just completed a mission and had not left the system map. I logged out, and logged into the RA5 to send the invite. RA5 was just outside of the trans warp gate in the Borg sector at the time. I switched back to the Trill and immediately received the invite, however, the trill was now also in Borg space.
This isn't at all game breaking, and I could just trans warp back to sol... but instead I've gone to the b'tran cluster and have been doing exploration missions. The Borg are pretty interesting to play against at this level: the weapons are scaled down, but they retain all the special abilities. Good times in a starter ship.