No, sir, the brisket can easily absorb too much smoke. I had a word the other night over this with the proprietor of a local BBQ house. The very best brisket from the legendary houses are not overwhelmed with this oily sort of taste. The "smoke ring" is overrated. One can get the best of it by the manner I've mentioned above (although it may not be the best method, granted). I recommend some experimentation with time, temperature and smoke. Getting it tender isn't that hard (after the first few), but regulating the flavor -- if you will -- is the difficulty.
Brisket is a cheap cut of meat. I eat it several times monthly, and an off flavor is too often found. One might say that there is the school lunchroom flavor (yes, we had BBQ brisket in Texas schools growing up), it is what the BBQ chains offer and it is none too good.
Then there is another step up where the smoke flavor predominates (generally oak) and it is too easy to overdo it.
Finally, there are those that have mastered it. But there are few houses, even here, where the man at the pit has been at it for long years. For those places we'll drive 100 miles round trip for lunch on a Saturday.