I had a related issue with my 5.3 after I purchased it, mostly the oil consumption problem. I never noticed any start-up smoke (but never looked for it either).
When I purchased the truck it had 164,000 miles and an unknown service history. It used oil excessively, about 1 qt/1000 miles with no apparent leaks. After a couple oil changes and many added quarts between changes, I searched for an explanation.
I found that in the TrailVoys, the 5.3, which is an Aluminum block, seemed to have a much worse than normal oil usage history. It seemed the iron block versions in the Pickups/Suburbans/Avalanches were not reporting the same level of the problem. Not sure that the aluminum block was the issue, I kept searching. I found that the PCV chamber inside the Driver side valve cover was faulted for sludging up easily and GM was replacing the Valve cover as a fix for the problem, a TSB (don't remember the number) is what I found.
I found and purchased a new GM valve cover w/new PCV for the drivers side. Put it on and have been seeing vastly decreased oil usage for the last 6,000 miles. Also, on top of this I have been driving aggressively (my normal routine) and as time goes by, it has also been idling and running smoother. I attribute the aggressive driving is helping clean the combustion chambers and rings. So after two 3,500 mile trips and needed maintenance my oil usage is down significantly. Last oil change at 4,000 miles and oil was barely low.
I am hoping for continued normal oil consumption. I thought about just replacing the PCV valve and agree it should help. I chose to replace the valve cover because my engine was extremely sludged (remember, unknown maintenance history) and according to the TSB the cover could not be effectively cleaned plus the PCV chamber had a probable seal failure that was mentioned in the TSB.