Right now the act requires them to register. It's a requirement for someone who's paid either as a consultant or as an in-house lobbyist. However, if someone chooses to put their name forward transparently to say that they've lobbied, whether they're paid or not, there's nothing in the registry that would stop someone from being able to do that if they wished to do so.
On May 14th, 2021. See this statement in context.