In this paper Monte Carlo Finite Element (MC FE) approximations for elliptic homogenization problems with random coefficients which oscillate on $n \in \mathbb{N}$ a-priori known, separated length scales are considered. The convergence of multilevel MC FE (MLMC FE) discretizations is analyzed. In particular, it is considered that the multilevel FE discretization resolves the nest physical length scale, but the coarsest FE mesh does not, ...