If it has a roof over it and the sides are screened, is that considered a "fence"? I wouldn't think so. It might just be a gazebo that happens to have chickens in it.
And if the screen just happens to have hardware cloth outside it...well...maybe you have some freakishly big mosquitoes you need to keep out of your gazebo.
All joking aside, if you built a chicken coop with an extended roof over the "screened" portion, I don't think that would technically constitute a fence since it would be a part of the building.

All joking aside, if you built a chicken coop with an extended roof over the "screened" portion, I don't think that would technically constitute a fence since it would be a part of the building.