If i had this setup, I would stir until i saw + signs of fermentation, then cut it off. Also, id only leave tin foil on the top until fermentation started, then add the air lock.
The difference between this and pumping air into the fermenter is that just stirring the beer doesnt draw any air into the carboy. al you are really doing is bringing the yeast underr the surface of the beer into contact with the air where it can absorb the O2. there will only be slight intake of air into the carboy from this method vs. actually pumping air into the carboy. thats why the 30 minute restriction on the air pump, and why I would use the stir bar until signs of fermentation start.