Do molecular orbital diagrams exist for ionically bonded compounds and molecules?
Molecular Orbital theory is a simplified approach to describe chemical bonding based on symmetries and orbital overlap. In principle, it makes no assumptions on the type of bonding, i.e., covalent, ionic, Van der Waals. This distinction is more a construct to understand the strength of the bond. 

In case of a covalent bond, the electrons that make up the bond are shared by both nuclei, whereas in an ionic bond the bonding originates mostly from the Coulomb interaction, that is, the electrons are mostly located on a single nucleus. In MO theory, this can be understood in terms of the interaction strength. When the atomic orbitals that make up the bond have similar energy (and same symmetry), there will be a strong interaction and the resulting MO will have character of both AOs. In other words, the electrons will be shared more or less equally by both atoms. When there is a large difference between the AOs, the resulting bonding MO will have mostly the character of the AO which is lowest in energy and as such the electrons in this MO stay mostly around this atom. This resembles an ionic bond.