Just as an experiment I set an ai flight from Germany to the UK, I activated TVB and Active Sky 6.
Watched the aircraft takeoff then as it reached about 5000ft I closed both Sky and TVB, both the programs carried on working throughout the flight, I thought that since I closed them it would either halt or revert the sim back to default settings and I would lose sight of the aircraft but no, so once loaded they must run in the background even after being closed.

If I remember correctly, Active Sky works by writing the information into the User Defined section in the weather settings, so shutting it down will just keep the weather from changing but won't erase the data already set in the sim.