When someone says a lens, or an optical system, resolves 2MP, it is 2MP @ 50% MTF (maximum contrast between adjacent pixels). 50% is the "good enough" of photography, but digital sensors and screens can be 100% MTF. Lenses can't do 100% but can get asymptotically near, so yes, using an "8MP" lens with 2MP sensor will show.

And, even considering 50% MTF, many professional lenses struggle to go beyond 3MP.