As users learn that Reddit links aren't useful sources of information, they'll click less, which means the relevance between the search term and Reddit goes down. Ultimately reducing Reddit's ranking, regardless of if the Googlebot is allowed to index the content.
People often mix up indexing and ranking. Indexing is if you're even in the results set, but ranking is where. Reddit might, technically, still be in the results set but if it isn't on page 1 for a given search it may have well not be.
The internet is becoming a friggin pain in the ass.
A better analogy might be Expert Exchange. A site that put answers behind a paywall, and fell hard out of Google's search results. Then Stackoverflow came along and took whatever remained.