If I have a script that checks for x connections every x minutes and blocks IP's after x connections will it stop Minecraft servers from working properly?
How many connections does the Minecraft client make to the server in one minute?
It depends, if you are connected and playing it only has one persistent connection. If you are on your server selection screen it will have a temporary connection once per refresh of the server selection screen.
So I guess a good estimate would be 2 + however many times you think someone will hit refresh on their server selection screen on average.