One would have thought so. However, all I can say, from experience, is that running two desktop environments on the same OS has, for me, never resulted in the same performance, for the lightest of those dekstop environments, as when it has been installed as a standalone desktop environment. For whatever reason, the dormant DE is somehow negatively affecting performance of the active DE relative to the usual expectations for it.
My guess to this would be background services/daemons installed because of the “native” DE of the distro that would still get called to run even if not needed by the secondary DE. This is only my own speculation though, not based on any form of knowledge of that.
That makes sense Rob.