AFAIK the csq is file based and they are persisted if the messaging provider is not available or down. IS checks for the messaging provider and once it is able to connect it will process the messages automatically in the order they are stored in csq, there is a setting for the same.
You can run a simple test and check the above scenarios on your local server. Let me know if you have any questions.
#webMethods#Universal-Messaging-Broker#Integration-Server-and-ESB