Two things happen, and OP nailed them both. A vacuum is not created in the sense that there is no air, (if there was air to beging with) rather the pressure will drop, due to the same volume of air occupying more space, and eventually it will stop, if it even started in the first place. So yeah, you need an air vent. as stated above.
Secondly, as the water level drops, the head height drops, the flow rate through the outlet drops. Chained reaction that equals the drip rate will change, and require adjustment probably.