You could do that, though I think you would be better served by a
half-barrel bell instead of a long pipe. No friction to speak of, and you can have the chimney right next to the combustion core to allow a bypass for starting. With a good chimney (maybe 10'/3m tall), you can get a fire drawing easily and then shut the bypass to put the heat through the bench. You can also have a solid masonry layer around the heat riser barrel so you don't have too much heat going out to the air but keep most of it for the bench.
I would probably make the core dimensions a bit larger (still 6" diameter), say 16" feed, 20" burn tunnel, and 48" riser, so you can use longer
wood and have to feed less often.
One thing you will have to work out is how to protect the core and bench from rain and snow. Using all brick instead of
cob might be
enough, or you might need some sort of roof.
I would make the chimney as a
plunger tube into the top of the half-barrel space, so the bottom of the tube can be raised or lowered to whatever gives the best balance of heating and drafting.