"Covering" a sensor is not the same as "Fully illuminating" a sensor. And even "Fully illuminating" is usually within some threshold. For example, a manufacturer may consider the fully illuminated image circle to be the point where the light drops off to 80%. But there is no standardization as to what these terms mean.
Then there's the "well corrected" circle, which is more or less free of aberrations such as coma. Point is, the area covered by the image circle will be different from the fully illuminated circle, which will be different from the well corrected circle. And manufacturers rarely specify all three.
But to your question, yes there is pretty much always some off-axis dimming with any scope, but it is more prevalent in scopes where the primary optic (mirror or objective lens) is far back from the front of the tube (including the dew shield on refractors).
Think of it like this. All stars are far enough away such that the rays striking the various points across the objective can be considered a parallel column of light. If a star is in the exact center of the field, then that column of light will strike the entire surface of the objective, regardless of any tube in front of it. But, if a star is a bit to one side of center, then the column of parallel light rays is entering the scope at an angle. Because of that angle, any sort of tube in front of the objective will shadow one edge of the light column and therefore reduce the amount of light hitting the objective.
A dew shield on a refractor is larger than the objective so it causes little off axis dimming until you get fairly far from the center. But on a reflector, the mirror is in the back of a fairly long tube, which is only a little larger than mirror, so that will cause more off axis dimming. Scopes like SCT's have baffle tubes which also makes it worse.