It is against code to reduce the pipe or flue size smaller than the outlet of the stove. Always buy the stove to match the chimney, and in the case of having a larger 8 inch chimney, reline it with 6 if at all possible and preferably insulate the liner.
That said, many reduced will physically work, but there are many factors such as chimney height, pipe configuration, atmospheric conditions, altitude, and the building configuration itself.
Bottom line is the chimney is the engine that drives the stove. It is not simply an exhaust for smoke. Just like an engine in a vehicle, it needs to be sized correctly for the stove so it doesn't need too much heat left up it to work, (the problem when the chimney is larger than stove outlet) or doesn't have enough capacity (in your case) to make the stove burn hard enough to heat the area you're heating.
The biggest issue, other than legality, is smoke roll in when opening doors to load. If the height of a taller chimney makes up for the smaller diameter (increases velocity, or draft) it may physically work. Like I said, there are many other factors.