A full primed pump will not have any air left in the pump basket but at lower flow rates it will take more time for the air to purge. I have a 1/2 HP pump and the flow rate is around 65 GPM. It will take sometimes 5 minutes for all the air to leave the pump basket but it eventually will. However, with a VS at full speed, it shouldn't take more than a couple of minutes for all the air to be purged.
What I mean by reduced suction is not reduced flow rate but reduced suction head loss as measured by "in-hg". Having the main drain and skimmer fully open reduces the suction head loss which in turn increases the flow rate so the pump should prime faster. But having higher suction head loss, will increase the suction at the pump basket (i.e. lower pressure) which in turn can draw in more air.
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