In Wrath of Kahn, the science vessel was looking for a dead world to use the genesis device on (it destroys anything used, therefore they needed a 'dead' world, but one with the right gravity, an atmosphere, ect. Anyway, the scientists thought they were on Ceti Alpha 6 which was dead. They then ran into Kahn and his crew which had been left on a beautiful primitive world with lots of promise (Ceti Alpha 5 - likely class 10-12). The problem was Ceti Alpha 6 exploded, and changed the orbit of Ceti Alpha 5 making it mostly barren (class 6). When Chekov stated to Kahn that he shouldn't be here since he was left on Ceti Alpha 5, Kahn growled that great quote in a mad fury "This IS Ceti Alpha 5!!".
The point is, a class 6 world can support life, but it would really SUCK.
Chris.