If you are using only a quart every 4-5K, then you have a pretty solid engine, certainly nothing to concern yourself with. Chances are it's just valve seals oozing a bit. My M103 used more than that when brand new.

As stated, the BG fuel cleaner should have limited effect on oil usage; unless the piston oil rings are gooed up and it clears that up. But only using the small amount of oil you stated, it's very unlikely the oil rings are the culprit.

The guys over on the Corvette forum like the BG injector cleaner, but they RAVE about Chevron Techron. So, this says to me either is good for cleaning out the fuel system. I buy the Techron at Costco by the 6-pack, and use it in all my cars every 6 months or so.

No need to change oil if you are just addding Techron it to your fuel.
I assume same applies for BG.

Now, if you are going hard-core, and add something like SeaFoam to the oil, or suck it into the intake, then you should definitely change the oil afterwards.

DG