Encipher, it doesn't really matter. Consider the extreme lack of orbital overlap between Cs and F as well as Li and I. Who cares that there is a finite positive degree of overlap? The point is that CsF and LiI are extremely hygroscopic to the point of deliquesence.
As for "covalent" bonds not being "completely" covalent, yes, this is true with many compounds that inept high school chem teachers call "covalent." However, we only really notice the "polarization" of the C-H bond in methane when running NMR with molecules that only show the inductive effect. Yes, the protons are waay upfield. Yes, the carbon is more shielded than it would be if the alkyl chain were more substituted, but what difference does it make in the chemistry of the molecule? It is at all nucleophilic? No. Electrophilic? No.
Concerning the previous response you gave that such atoms as aluminum are commonly found in +3 ionic or "semi-ionic" or "very polar covalent" states, I must respectfully disagree. Trivalent (NOT ionic) aluminum is a very useful Lewis acid and such reactions as the Weinreb amidation would not proceed without this property. As well, the reduction of amides, esters, and carboxylates would not proceed if not for the fact that Al is not at all inclined to be in a cationic state. Moreover, it generally takes on a negative forma charge and in fact, its acidity can be observed by its reaction with water:
2AlCl3+3H2O-->6HCl+Al2O3