You don't want air in the supply b/c if it works it's way into the oil pump, the pump will cavitate. It may be necessary to disconnect the inlet tube from the pump and hold it up to bleed the air out then quickly reconnect it.
At low throttle angles (as in the case of ski/boat a trailer out of the water) where the tension on the oil pump cable is relaxed, there's virtually no oil being pumped under these circumstances. You have to rotate the pump valve lever manually open and run the engine to get flow.
If you still are unsure if the oiling system is purged and operating properly, you can pre-mix the fuel until you're confident the oiling system is functioning properly, too much oil doesn't hurt anything other than it might oil-foul the spark plugs.