AFAIK Fleets don't care about stars if the sector doesn't have a player in it. you can "park" your ships in the core of a star and they won't care unless a player comes to visit. You can ignore stars in most fleet operations because of that.
This is correct. The fleet will only actually "exist" as long as it is in loaded space (space within a couple sectors of an active player). Once it gets out of that range, it unloads along with everything else and the system just calculates where it should be given maximum speed and has the ships re-appear at the destination (assuming someone is there to see them) after the appropriate amount of time.
So unless there are players sitting in the path of the fleet forcing it to remain loaded, stars and planets aren't an issue.
On a side note, this is also an EXCELLENT way to get somewhere safely yourself. Put yourself on a ship in a fleet, command the fleet to move somewhere, then log out. The ship will unload, and in however much longer later it gets to the destination you log back in, and bam, you're there.