The Consortium Surveys mostly choose to avoid the intrinsically faintest stars, therefore the low-mass end of the main sequence, however in some cases, the selection criteria will be based on parallax information and apparent magnitude only (e.g. main sub-surveys of the Milky Way Bulge and Disk Low-Resolution Survey). In the effort to fully sample one particular component of the Galaxy such as the Galactic disk, while on the other hand attempting to be as unbiased as possible, such observing strategies may encompass many different spectral classes of stars, including the low-mass regime.
4MOST limitations in this regard have to do with the standard compromise between the intrinsic luminosity of the targets, their distance, and exposure time, which have to be considered individually for each science case. The 4FS ETC (4MOST Facility Simulator Exposure Time Calculator) should be consulted to address the feasibility of observations of low-mass stars given the expected quality of resulting spectra.