I have one of my Ashfords on a pretty short chimney, surely well under 15 feet, maybe as short as 12 feet. It's some work getting it to draft above 40F, and if I'm not careful to establish draft before lighting a load, I can have the family yelling at me about the smoke. But it's never been a problem to get it drafting, usually by lighting something small first, and holding it farther back in the stove to heat the chimney. The only real problem in this operation is my own attention and memory, namely forgetting to establish draft on a dead-cold stove, before loading full and lighting it on a 50F evening.
It will also limit how far you can turn down before stalling, but that's been a problem more in theory than practicality for me, I can still run that stove pretty darn low and slow.
Spill-out from the door hasn't been any issue, as the chimney is usually pretty warm when I'm opening the door. How often do you open the door on a load of wood that's still producing smoke, when the chimney also happens to be cold? Never, in my case.