You'd get the same resolution because colour cameras interpolate (demosaicing). If you converted to grayscale you might get problems because each pixel has a different colour response with the bayer filter. You'd still need to do some intensity correction.
The performance of the Leica Monochrom is due to this - you don't get more pixels per sensor, but you get proper intensity values at each pixel. This corresponds to better effective spatial resolution in most cases. All they're doing is selling you an identical sensor and pretending it's something fancy and new...
When you buy industrial cameras, the colour and mono versions are identical, but one is filtered (they use the same detector). We use mono in industry often because image quality tends to be much better than colour, and you have a third of the bandwidth requirements (or you want to filter a specific waveband).
