Is there any way to create and deploy an event receiver onto a sharepoint site using only the NAPA development tools and an O365 development site? If not, is there any way to create and deploy an event receiver using Visual Studio 2013 with only a O365 development site and no local sharepoint development server?
Since your question has references to "NAPA", "local SharePoint development server", so I assume you are asking about Remote Event Receivers. Apps developed using NAPA are SharePoint-Hosted apps and SharePoint Hosted apps don't contain remote event receivers. Moreover in NAPA you can add few file types only like .js, .css and web pages only.
In SharePoint 2013, the code that runs when the event is triggered is served by a web service. This means that if you register a remote event receiver, you also need to tell SharePoint which web service to invoke.
So you can create remote event receiver using VS 2013 and O365 but you need a site apart from SharePoint site which will host the service for remote event receiver. This is the reason if a remote event receiver is added to a SharePoint-Hosted app, it immediately changes into cloud hosted app and adds a web application project as well.