In a pure Dyson shell surrounding a non-moving star, with the shell rotating around the star, could the centripetal force of the shell act in some way similar to gravity toward the interior of the shell. it's not a field force, so i would assume not, as there is no way it would act on an object that is not part of it.
Overall, no, not if you're talking about a "classical" Dyson sphere: a rigid spherical shell. At the equator, centrifugal force will act as a pseudo-gravity for anything making contact with it or coupled to its rotation, so atmosphere will behave approximately correctly. Atmosphere is viscously coupled to the rotating surface, so it gets carried along.
The problem is that, as you move toward the poles, the apparent "gravity" will gradually become both weaker (as the radius of rotation becomes less) and tilted away from local vertical. The direction of the centrifugal force will always be in the plane of rotation, and that will always be parallel to the equatorial plane. At the poles there will be no effect at all, since the moment arm of motion will become zero.
As a result, as you move away from the equator the air will get thinner and the local "gravity" will tilt more and more toward the horizontal at the same time as it gets weaker.
Of course, a Dyson Sphere is pretty big, so there's a lot of equator. Presumably a band of several degrees of latitude will be useable, and that will have an area many times that of earth.