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.
On a lot of the photography forums, people talk about how much a lens "out resolves the camera's sensor", meaning that any improvement in the lens will go unnoticed until they upgrade the sensor. They often use the DXOMARK score (perceived megapixels?) as a metric of this. It seems to make sense but I really have no idea how much truth is behind this!