I disagree 100% with swearingen. Are you going to give them reactions for every load case (dead, live, wind in one direction, wind in the other direction, component and cladding wind, same for seismic, etc) and expect them to figure out which load combination produces the worst result? Good luck in getting the "right" answer.
The AISC Code of Standard Practice says the engineer of record is to provide data pertaining to loads (which I suppose would make swearingen's proposal "acceptable") and which methodology (ASD or LRFD) to use. If you've designed the building with LRFD, I can't think of any reason not to use LRFD for the connection design forces.
To answer the original questions:
We use whichever one we used to design the building.
and
It could very well be acceptable, but I would think it best to use the same method for both.