The resolution would be the same. The demosaicing algorithms involve weighted summing of neighboring pixels (essentially very specific weighted-averaging of 3-by-3 (usually) pixel blocks).
But unlike other typical instances of pixel summing or averaging, sensor demosaicing does not involve a downscaling of spatial information.
Now, because the demosaicing algorithm is essentially trying to create (interpolate) data that wasn't captured, there are some noticeable effects or artifacts if the color information in the scene changes rapidly (specifically, near the resolution limit of the sensor). Because the spatial frequency of (typically) red- and blue-filtered sensor pixels is 1/4 the sensor's absolute spatial frequency, the color-specific spatial resolution of the output image is correspondingly reduced.
But in terms of absolute pixel spatial resolution, CFA sensors and pure-gray sensors, built to the same pixel pitch, spacing, and dimensions, will have the same pixel resolution1.
- The effective pixel area of CFA sensors is (at least) 2 pixels fewer in each dimension (1 additional pixel on each edge) than the actual pixel count on die. This is so that the edge pixels in the produced image all have neighbor values to use the same weighted-summing demosaicing. Without the "border" pixels on the sensor area, the edge pixels in the produced image won't have had data from the non-existent neighbor pixels past the edge. These extra pixels are like an unusable "picture frame" of pixels on the sensor die; they don't count in the produced megapixels of the final image.