I gave something like that a thought, but we go to some trouble to get the stack size just right. I figured adding a piece to it would effect temps and draw. Not so?
Yes, extending the stack vertically does increase the draft. You can compensate by throttling down the cross-sectional area or reducing your fire box intake but if you're real happy where you are, you may not want to start twirling knobs.
But keep in mind any exhaust fan is essentially doing the same thing, particularly if you're working/pumping hard to suck away smoke. In theory, the top of a normal stack in an open space is taken as a zero pressure point so what you're doing with a fan is putting negative pressure, or vacuum, at that same vertical point to suck the smoke someplace else. That new negative pressure point would have corresponded to a point further down the stack before (with peak negative pressure being at your intake) so you've essentially lengthened the stack even though its physical length appears unchanged.
Yes, that's a pellet machine in the picture with the dryer hose and yes they all use forced air to get the fire going. But you'll notice a string of switches under my hopper to throttle that forced air down to natural draft in 7 steps.
And for minimal upset to your present draft, you'll want such variability in a fan-based exhaust. Run the fans low, and let your pavilion smoke up, to most closely mimic the open-air design of your smoker. Then when you want to go inside, run the fans for a minute to clear out the smoke, knowing you're temporarily increasing the draft from its design value.
By the Bernoulli effect, something similar happens when a breeze goes horizontally past an open stack. (The added convection of the wind also increases the heat flow out the walls of the smoker.) But we get to know our machines pretty well even if we don't recognize all the physics at play, and we just get the job done. In other words, there's a little knob-twirling going on in life whether we like it or not. We go with the flow, pun intended.