When I searched for the same thing, there were people split between sealing halting any aging, and those saying it helped.
I would imagine it adds more protection. And doesn't lack anything, because aging in a carboy with airlock doesn't exactly allow the transfer of air. I doubt a cork transfers much if any.
Yes wax seal would be better, imo. Shrink wrap i'm sure can be airtight but it'd also be more prone to easier puncture. Just make sure you get a good coat of wax and that it doesn't crack while cooling.
I was going to use beeswax on mine, but wound up not sealing any. But I see no advantage to paying for a synthetic wax when I can get beeswax from my hives. I doubt theres much if any difference in the seal they produce.
Storage. I'd imagine sealed you could store upright, but if the cork does dry out then all you are relying on is a beeswax seal. But maybe somebody has tested it both ways.