What happens when we exceed limit of licensed users?

I think the documentation you have read is correct. After all, what else would you expect? If licensing limits are exceeded something has to happen, outcomes are (a) everything stops, (b) usability restrictions are enforced. I think this is a reasonable outcome? For reference JIRA goes readonly, you can see issues but you can't create issues, the parallel is pretty clear!

While we are in the throws of purchasing a new license, has anyone discovered a way to stop people registering and breaching the license limit?

Just to add a comment on this. I have found and confirmed in the older versions (haven't confirmed in the newer versions, so I won't comment on them) that confluence becomes read-only at "license count - 1". In my opinion if I have a 100 user license, I should be able to use the system fully as long as I have 100 or less users in the system. If i try and add a user and increase the license count to 101, then I can see it complaining. That makes sense. That is not how it works. In reality I can only use 99 user licenses. I know that this is a fairly minor point, but it something to keep in mind. I've mentioned this to Atlassian before, but they don't think that this is a issue. I happen to disagree, but I seem to be the only one who thinks this way.