The woodstove sits by the exterior wall. To make the chimney exit at the highest point of the roof – per installer – the chimney is routed under the roof for about 4-5 feet at an angle, from the edge of the roof to the center highest point following the  sloping ceiling (pitched roof). There is no attic – so the sloping ceiling has insulation etc, between the drywall and the roof. 

Now to hide the chimney, a dropped ceiling has been proposed. From what I understand, that would mean that the chimney is now routed via a semi-conditioned space.

Is that a problem? 
do I need to worry about the space itself (humidity? Anything)?