Quick-and-Dirty Molecular Dynamics by Mass-Weighted Atom Translations?
The random displacements in your suggested method are uncorrelated from step to step.  What you are suggesting is essentially heavily damped molecular dynamics at the Brownian limit.  The limitations are obvious, you won't sample correlated, large-scale motions efficiently.  (That might be a student project right there: turn up the Langevin parameter, see when you lose rotations of phenyl rings, and ask yourself what this means.)