Interesting thread to read though.
@karam explains it well. The answer for me is "sometimes" but very rarely. In tall pipes more often than others.
The flavour we chase comes from that place just below the ember where those "volatile compounds" (the aromatics) become vapour - which is also why I smoke as slowly as possible and aim for that light and powdery white/grey ash. Relatedly I would assume it's also why some flakes seem to smoke better just a little damp.
Surely a properly packed pipe (with whatever cut or stuffing method) and a good ember will let that ash balance on top of it and protect the ember all the way down... but that's in a well-packed pipe.
Sometimes we have to problem solve, and that's usually when I might choose to dump some ash, put it down for a while and then pick it back up and get it going again. That second part of the smoke isn't usually as good.
That said, I dislike stirring up old ashes and aim to go without dumping.