Do chemists use molecular orbital theory to explain physical characteristics of a compound (i.e. melting point, boiling point, etc)
Certainly the electronic structure of compounds are of interest when predicting or interpreting the physical properties - but not necessarily the molecular orbital theory in and by itself. The symmetry of compounds (and by extension this also means;) the symmetry of the bonds in the compound are vital to many physical properties. However, MO theory is mainly used to describe bonding in more detail, not to infer "macro"-properties FROM bonding - so I guess the answer is... "no and yes". Yes, chemists think about these things, at least the ones that work close to the quantum realm. No, MO theory is not really useful in the way you are describing - with one giant exception:

When we are talking about "possible" physical properties of not-yet-synthesized compounds, the answer is resoundingly "yes". Graphene, for instance, has more theoretically predicted qualities than have been measured. Super conductance, tensile strengths, diffusion rates... there is just so much exiting being suggested all a result of computer modeling on the quantum level from MO theory and the likes.