Can this leader still do missions? What is the penalty for them being there?

You can only assign leaders in the leader pool to missions. And only during the assignment phase. So a leader on the base will not be able to do missions. They would be returned to the leader pool during the Refresh phase.

There's no penalty. Basically it's just to represent that they made their escape and are harder to recapture (since there's at least two leaders together in a system with no imps present)