This is very much a use case that Omeka S attempts to address, so yes, it is a valid approach. The Dspace Connector and Fedora Connector modules very much have this situation in mind (though we’re still noodling through the details). Both of those, however, pull into Omeka S via the module, rather than push from another system.
A push mechanism on the Dataverse side would have to use the Omeka S API. That, too, is entirely within not just valid, but encouraged, approaches to using Omeka S.
Visualization moves into the realm of theming. It sounds like there might be some custom theming to do for your particular datasets, depending on your particular needs.