OCS is not as completely foreign to Russian speakers as Old English is to English speakers; I would compare it more to Chaucer than to Beowulf, although whether you can understand a specific text depends very much on the subject and the context. Since Biblical quotes and expressions are so common, OCS terms may be familiar to even secular Russians.
Note, however, that OCS does not have an ancestral relationship to Russian - it is a Southern Slavic language, most similar to ancestors of today's Bulgarian. Old Russian texts (such as The Tale of Igor) are written in a different language - Old Russian (which existed long before the split into Russian, Ukrainian and so on, so the name "Old East Slavic" is sometimes used).
Note, however, that OCS does not have an ancestral relationship to Russian - it is a Southern Slavic language, most similar to ancestors of today's Bulgarian. Old Russian texts (such as The Tale of Igor) are written in a different language - Old Russian (which existed long before the split into Russian, Ukrainian and so on, so the name "Old East Slavic" is sometimes used).