I do believe the charcoal must be the key. No, the ring doesn't matter in the taste at all. It only matters when a "friend" points out that - "oh, dear, there's no smoke ring in YOURS" - that's when I first noticed it. Then when I smoked the first butt in my other smoker - poof - smoke ring. So, for whatever reason, it is the charcoal or hardwood briquettes like I use, that causes the smoke ring.
The friend that pointed this out brought a smoked pork butt to the same function I did. Hers had a beautiful smoke ring. However, she doesn't smoke with any hickory or any wood, only charcoal. I'd rather have no smoke ring and good flavor
And, if you ask any hardcore smoker the smoke ring is kind of like a badge of honor - and does make a difference to them.