I (a non-Slavic language speaker) would imagine the divergence between the modern Slavic languages would be dwarfed by the divergence between those languages and Proto-Slavic or Old Church Slavonic.
Quite the opposite, I believe. My native tongue is Polish (West Slavic) and I speak decent Russian (East Slavic) as a foreign language. My subjective feeling is that there's more in common between either of those languages and OCS than between the two directly.