I did some testing based on Exchange off-box but the results are going to be the same. I stopped IIS Admin service and of course all the dependencies. During this outage, new messages left are not available. I restarted the IIS Admin service, along with each of the dependencies. The last services I turned back on were Microsoft Exchange Routing Engine and SMTP services, and only then the new messages showed up.
As for messages that were left prior to stopping IIS Admin, they were available. The MWI also turned off after I deleted the messages.