With the typical slip fit of normal (Colt spec) parts I can't see any point in doing that. Oil will seep between the barrel extension and the barrel extension socket of the upper. On assembly what you don't want is lube between the rear facing side of the barrel extension flange and the contacting socket face of the upper. The more friction there the better so that the surfaces are less likely to slide on each other while applying torque to the barrel nut. However, you do need to liberally apply grease to the front facing side of the barrel extension flange that contacts the clamping surface of the barrel nut to reduce friction as much as possible so it doesn't drag and seize up.
And YES to the liberal application of grease on the threads of the upper.
On a thermal fit upper I might oil the external surface of the barrel extension and blow it off with the air compressor before putting it in the upper, but no grease.
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