They really should not! (or at least internally) I am involved with installing "chimneys" often through flat roofs. (actually Pneumatic Tube stations in hospitals, which often have the tube routed out of a ward through the roof and cross to somewhere else outside). These will be 110mm and 160mm tubes. I can guarantee you that if we don't intentionally valve off the tube so it doesn't have an open end exposed to the room, we end up with a condenser. The warm humid air from the room goes in to the open end, rises and condenses in the tube as it passes to the cool outside, and runs back down.
If the room is pressurised (e.g. manufacturing Pharmacy) we have to weight the valves to above room pressure to make sure they are closed when the system is dormant.
This is exactly the same as a chimney - an opening to a warm room which allows room air to rise to a cold area. Same problem - you get condense where the warm rising air hits the dew point.
I'd not be too worried about a bit of condensation if the chimney is ventilated. Worse is to trap it in there if/when water penetrates into the chimney or the humid air permeates through from the house.
Ventilation ducting is a bit different due to the intentional extraction of humid air and the higher flow rates.
But my highest preference is to ventilation from the outside to avoid the issue as I showed in my diagram.
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