There are many debates over the actual function of the transfer valve as well as plugging it.
If you plug it, theoretically no more oil should enter the primary due to sit sumping. Read more on Sit Sumping in the Sportsterpedia.
Normally, if the bike does wet sump, excess oil will trickle into the primary case. ¹⁾
When you start the engine, the return oil system will gradually empty the contents of the crank cases back to the tank.
It will also shoot excess oil out through the gear case breather onto your clean floor.
Once the excess oil is removed from the crank cases it will start drawing oil in through the transfer valve until the oil level is returned to it's correct level.
At that point, your oil tank should have returned to it's correct level and the engine should be running normally.
The transfer valve also allows oil to flow from the primary back into the crankcase if the sprocket shaft seal was leaking.
²⁾

Excess oil gets into the primary through a bad crank seal or poor sealing of the oil pump.
Keep in mind that drain oil from the top end also comes down the pushrod tubes and settles in the gearcase and down the holes in the cylinders into the crankcase.
Any oil that gets in the gearcase floods the oil pump scavenge inlet and runs back into the crankcase oil slot.

But, the oil was originally in the tank when the engine was shut off last.
It gets to the crankcase thru normal top end drainage, the check valve or oil seal issues in the oil pump, flooding the oil trap, then to the crankcase, up the wall and into the primary thru the transfer valve.
So plugging the transfer valve only addresses issues with oil getting into the primary from the crankcase but doesn't address excess oil getting into the crankcase.
These are separate and equally important issues.

Main reasons for plugging the transfer valve:

• To stop oil from filling the primary compartment when the engine sits for a while.
• To enable you to run separate oils in the primary and the engine without cross contamination. ³⁾
• To run the primary dry. People do that to run belts (even though it's not necessary). ⁴⁾

So there is technically no need to have the transfer function to remove sumped oil from the primary.
However, if the crank seal blows out, you'll end up with a primary full of oil and lower oil flow to the engine due to half of the oil being in the primary.
But that's a separate issue you'd have to fix with or without the transfer valve functioning.

Quote from thefrenchowl of the XLFORUM ⁵⁾

H-D called this an “oil transfer valve” from its 1st application on the K model where indeed it acted as a suck valve for excess oil in the tranny due to a poor oil seal design on the engine sprocket. It had a tube attached to it, bent down towards the bottom of the sprocket. When oil level was normal in the tranny, it just sucked air. When the oil level went up, it submerged the tube and the vacuum in the crank cases sucked out the excess in the crank cases. The bad sealing idea was discarded in '54 and replaced with a proper lip seal and our unloved transfer valve. The guy who designed it is an unsung genius, cause it's real purpose, intended or not, wasn't discovered until the factory got rid of it in the late 70s. That's when they noticed that bikes which did not see constant use got various amounts of rust building up in the tranny, despite it having the small hole breather in the filler alloy cap and a special vent bolt installed on top of the tranny. A new problem they never experienced in the past engines. They then discovered there was little air circulation despite the 2 vents in these trannies and moisture stayed in to do the damage. In earlier engines, air is constantly being replaced in the tranny by the one way valve/crankcase vacuum and moisture can escape. So, if you use your bike daily, by all means, discard (the transfer valve). Personnally, I think it's a great idea and never experienced its failure in all the years I've been riding Iron Sporties or Ks, nearly 30 years now. If a part is in there, it's got a purpose. I've had too much oil in the tranny as anybody has experienced, but it's always been a seal failure, nothing to do with the transfer valve.

See Removing / Installing the Transfer Valve in the Sportsterpedia.