I highly doubt that the meat could get too much smoke of any kind. I shovel the coals up under the meat from a burn down pit, just like every pit boss at every NC bbq joint that still uses wood. If you look at the link I provided with my first post in this thread, you will see my pit, and that my pit is not an open pit- the smoke has to travel from the coals, around the meat, and swirl up to a small vent.
As the meat heats up- starting at around 180 F., every 30 seconds or so, you will hear the sizzle sound from the occasional fat dripping. To be honest, I doubt this slow dripping and sizzling adds much flavor from the smoke
rising after the fat dripping burns up. The dripping does increase the flavor, because the sound signifies that the shoulder is now hot enough to render the fat- and that fat leaves flavor behind as it bastes the meat.
Now, if I only shoveled coals, I would only generate minimal smokiness. The coals that heat the meat are very clean. They produce very little smoke, blue or otherwise. If I stopped at this point, the meat would lack the smoke flavor. I exponentially increase the smoke flavor by adding unburnt wood. When I split the hickory logs with an axe or maul, I always end up missing the mark sometimes, sending thin splits and shards flying. After splitting the wood, I collect these shards in a grocery bag, and throw them on the coals after I put the shoulder on the grate. It only takes a few every hour or so to create a massive amount of smoke. Where you might only see a few wisps of thin blue smoke before, with these lumps of hickory wood, the smoke is very thick and billowy. It is sometimes blue and sometimes white, and that is okay. The only thing you really have to worry about is keeping the shards of smouldering wood from catching fire. I would highly recommend doing this, because there simply is not much smokiness generated by simply shoveling the burnt coals under the grate.
Honestly, I wish I could create the situation where there is simply too much smoke flavor (ala Allen and Son BBQ.) With that extreme conquered, I could then find a happy middle ground and keep it there consistently.
Here is a link to the Holy Smoke BBQ song:
What smells so good?
Is someone burnin’ hickory wood?
What's that cookin' on those coals?
Why it's a pig! Lord bless my soul!
We're gonna have some barbecue.
Boiled potatoes. Brunswick stew.
Slaw that's white or maybe red.
Hush puppies or fried cornbread.
And sauce from an old recipe
known only to the family.
A great big glass of sweet iced tea.
Holy smoke! That's heav'n to me.
—from Holy Smoke