If a player sends any messages through any chat system in the client - whether that is in-game or out - those chat messages are logged. When you report someone for verbal abuse, that particular game is flagged for review. This includes all chat associated with that game, including pre- and post-game chat.
We obviously don't have specifics on how the automated system works (which is good, since otherwise people could learn how to avoid bans while still being toxic). However, based on the collective experience of myself and stories I've read on the official forums and Reddit, I would estimate it works similar to this: In most cases, the automated system will examine the logs for toxic behavior (usually looking for specific keywords, such as racial or homophobic slurs) and will then issue bans if necessary. If a single player gets reported enough times, the automated system might ban them, or it might escalate to a Riot employee for a manual review. In either case, the system and the Riot employee have full access to all data about the game, so it's easy for them to see whether a player should be banned or not.
So yes, if you see toxic behavior in the game, report that player. Riot definitely gets all the data necessary.
Side note: You can even report a player if they are abusing you when no game occurred. For example, if you get a friend request from someone and you accept, and they send you a bunch of spam or verbal abuse or something like that, you can report them via Riot's support page.