Some engines will use almost no oil, while others will use some. If you are using a quart every 2200 miles, this is not considered excessive.
DEFINITION: Excessive oil consumption (not due to leaks) is the use of 0.946 L (1 qt) or more of engine oil within 3 200 km (2,000 mi).
In my opinion, the engine should not use that much oil, but according to GM, it is within their guidelines. There is a technical service bulletin out that deals with exhaust valve stem seals on this engine that may not stay in place, causing excessive oil consumption. I have included this bulletin for you.
#05-06-01-035A: L26, L32, L36, L67 Excessive Oil Consumption (Replace Exhaust Valve Stem Seals) - (Oct 2, 2007)
This bulletin is being revised to update the model years. Please discard Corporate Bulletin Number 05-06-01-035 (Section 06 -- Engine/Propulsion System).
Some customers may comment on excessive oil consumption on 3800 Series II and Series III engines. An engine that has excessive oil consumption uses 0.9L (1 qt) of oil or more within 3 200 km (2,000 mi).
This condition may be caused by the retaining ring on the exhaust valve stem seal not securely holding the seal on the cylinder head boss. If this occurs, the exhaust valve stem seal(s) may move off the cylinder head boss and no longer provide a sealing function between the exhaust valve stem and the valve guide.
Notice: Oversize valve stem seals are available. Make sure the correct valve stem seals are installed. An OIL CONSUMPTION concern can be created by installing the oversize valve stem seals. The oversize valve stem seals are marked black in color and are NOT to be used UNLESS installing valves with oversize valve stems.
Notice: There are 2 different valve stem seals used - one for exhaust valves and one for intake valves. Exhaust valve stem seals are green in color and have "EX" molded into the top of the seal. Intake valve stem seals are blue in color and have "IN" molded into the top of the seal. Using the wrong seal on a exhaust or intake valve can also contribute to oil consumption. The correct seal usage should be verified while checking for correctly seated exhaust valve stem seals.
*Seal, Exhaust Valve
*Exhaust valve seals are five seals to a package. An additional package will be needed so all six exhaust valve seals are replaced.
While this is a possibility, it is not likely. Ring sealing technology has come a long way and we don't see many problems with this. The exhaust valve stem seal problem is common on this engine.