Let's say we have a native Russian speaker, who never learned or heard Church Slavonic. If he listens to a text in this language (I mean contemporary CS as used by today's Orthodox Church and with Russian pronunciation), how much would he understand?
I believe there is no "correct" answer to this question: too much depends on other qualities of a person in question, such as having "a good ear" to languages and knowing other Slavic tongues. As already discussed, many Russians claim to understand Ukrainian and even Polish and Bulgarian, but practical experiments show that this is not a common place.
Having dealt with Church Slavonic a little, both written and spoken, I can say for myself that it is basically not understandable. In a church, people often understand it "by context" and would probably be unable to explain what a particular word means. But even more so, they are just used to express some feelings using particular words (prayers), and would be unable to express or understand anything else using the same vocabulary.
A typical example is a traditional Easter greeting in Russia, Христос воскресе!. We do not say Христос воскрес! because it would immediately make it non-religious, which is an important aspect of this phrase. However in no other context would a normal person use the form воскресе.
One can compare this situation with the use of Latin in medicine. Although doctors traditionally study this language and even use it in daily practice, most of them would probably be unable to understand Horatius or Vergilius without translation.
Not sure if it answers your question, though.
Russian has borrowed very much from CS, and CS was influenced by Russian too (though to much lesser extent of course).
There two aspects in understanding: grammar and vocabulary.
CS words can be split into the following categories:
Russian loanwords (borrowed from CS into Russian) with Russian correspondense lost or rarely used, also words which have not diverged: священник, время, плен, нужда, враг, одежда etc. Those words are best comprehended.
CS words not diverged with Russian or with Russian parallels: чаша, огнь, сребро, крава etc. Those are understood quite easily (but of course better with some practice).
Russian loanwords which diverged in meaning: колодезь/кладезь, горячий/горящий, текучий/текущий, сиять/зиять etc. Those are comprehensible but can cause trouble in picking correct meaning.
Words with Russian correspondense diverged in meaning but not form: язык, глагол, муж, жена, честный, бремя etc. Those words are comprehensible but can cause serious trouble due to conflicting Russian semantics.
Words with no direct Russian correspondence: mostly functional parts of speech, but also pronouns, adverbs and some verbs and nouns too: егда, иже, паки; брашно, вретище, мирница etc. Those are the hardest.
The grammar of CS is very different in all aspects: verbs govern other cases, tenses have changed completely etc, postfixes do not correspond to Russian ones etc. This is also a very hard part.
I just picked a random Bible quote (Judith 5:9, in modern orthography):
И рече Бог их: да изыдут от пришествия своего и да идут в землю Ханааню, и вселишася тамо, и умножишася златом и сребром и скоты многими зело
which in translation would give
Но Бог их сказал, чтобы они вышли из места переселения и шли в землю Ханаанскую; они поселились там и весьма обогатились золотом, серебром и множеством скота.
or, in KJV
Then their God commanded them to depart from the place where they sojourned, and to go into the land of Canaan: where they dwelt, and were increased with gold and silver, and with very much cattle.
So we have:
- Changed tense in сказал
- Changed prefix, tense and government in вышли
- Пришествие was loaned and changed meaning
- Changed tense in идут
- Ханаанскую changed suffix and postfix
- поселились changed tense and prefix
- Умножать was loaned and changed meaning; also tense
- Зело is incomprehensible in Russian
So an "average" Russian would probably understand the following: God did something and there was a trip (by someone) to somewhere called земля Ханааня and there was a settlement there which dealt somehow with gold, silver and lots of cattle (or probably rude people).
The Church Slavonic is an artifical language created by orthodox missioners. It was based on southern-bulgarian dialect of slavonic language native to Saints Cyril and Methodius who created it. Its grammar is influenced by Greek language in both sentence structure and word structure. It looks like it is similar to Russian but it isn't so similar. And native russian speakers are making a lot of mistakes when trying to understand it. There are a lof of paronyms, words that different meanings in both languages. For example "живот" is "жизнь" in russian. Some words can have completely opposite meaning, for example "непостоянный" in russian is "inconstant" but in CS it is "The one whom nobody can withstand against"
I can give you a precise anecdote about old slavic ( not exactly church slavonic but I think this should be the same language ).
One day in Ukraine I was showed a old slavic book by a friend ( which was perfectly understanding Russian ). We even couldn't understand what the book was about. Not only the language was different from Russian language but also the alphabet. So anyway my Friend couldn't understand anything, or just some words that looked familiar to him, same I saw indeed some words looking the same or almost the same than in Russian but that was just maybe 1% of the worlds, the rest looking like code . We had to send scanned copies to a old slavic language specialist so that we could get an understanding of the text (which appeared to be an interesting text of rules for a monastery) . Honnestly I would say it is very hard ( and in fact practically imposible ) to understand Old Russian Slavic for the normal Russian person.