No, the game is never unbeatable due to inaccessible exit beacons. There should also never be an inaccessible quest beacon. However inaccessible beacons do exist, and it's by design.
From Matthew Davis, developer of FTL:
I miss when games weren't laundry lists to check off things to do as I worked my way through it without issue. In the "old days" it might have been due to bugs, design, or just my flawed memory, but I preferred worlds where sometimes quests wouldn't be solve-able and not every location was reachable. It made the world feel whole and complete. Like there was more going on than the player was privy to... I don't see it as a problem. FTL has had this for 12 months, it's been left for a reason :-/
On the other hand, quests were never intended to spawn at unreachable locations and that should have been fixed as of the last patch. And the exit should always be reachable (which was the original purpose of this thread). So if those bugs show up please show me screenshots / send me saves.