Registration Validator will only record IP addresses during registration under normal logging levels (under verbose or debug it will log all IP addresses - but you won't be able to match them to a user account as that information isn't needed by RV). So if there is a problem user, RV by itself won't be a great help (but then, it is designed only as a registration protection utility).
Adding the IP address(es) to the block list once a user account has been deleted will prevent them signing up again from the same IP address. However, depending upon the user this may also not be a very effective defence - it is not very difficult to obtain a new IP address (either by using a proxy or if your internet connection has dynamic IP). RV does try and determine the actual source IP as opposed to any proxies, but this information may not be available and may also be modified quite easily.