I'm not asking how to do it, I'm just asking about a potential change of headspace.

I have a complete Bushmaster DCM upper that has the competition sight on the upper with the carry handle (not detachable).

I also have a brand new Tactical Machine bare upper that has the rail for a scope.

All I want to do is change out the uppers so that I can scope the DCM upper.

My question is; since I'm using the same barrel assy. and bolt, will changing out just the upper potentially change the headspace of the barrel/bolt?

Unless the new upper somehow affects the bolt  locking into the barrel extension, there shouldn't be any issues.

Just FYI, that front sight may well be brazed onto the barrel. A total PITA to swap everything out. Get yourself a gasblock to go along with the upper receiver.

No.  Headspace is a function of the dimensions of the interface between the bolt and barrel extension/barrel.  Theoretically, something out of whack with an upper could prevent the bolt from fully going into battery (something preventing full travel of the carrier), but the gun wouldn’t be able to fire in that condition (and it would be immediately apparent).