Advantage of Pausing SQL Server
When you pause an instance of Microsoft SQL Server, users that are connected to the server can finish tasks, but new connections are not allowed. For example, you can pause an instance of SQL Server for a few minutes and send a shutdown message to connected users before shutting it down and then shut it down once all the processes are completed or rolled back by users. This way will ensure that there is absolutely no impact on users from a planned shut down of SQL Server.
You can also resume a SQL Server service after it is paused without shutting it down. In this case, SQL Server will start accepting new connection as soon as the services will enter to running state.