Well, I don't know about MDS, but maybe one could use parallel coordinates to visualize the population data and then overlay the estimated means and covariances of the GMM. For each component of your GMM, visualizing the mean is trivial. For the covariances, you can at least mark the covariance range around the mean at the i-th dimension's axis with the according element from the diagonal of the covariance matrix. This method might already give you some idea about how well the GMM models your data. Of course this doesn't really show you the (i,j)-covariances for i != j, but I guess those could be explored too by interactively moving the i- and the j-axis of interest next to each other and range-marking the space in-between them by the according i,j-cov value.
Haven't tried it (yet), and maybe there's some issue with this idea I didn't think of (if so, please correct me), but I think it's worth a shot.