Application integration concerns

Do you think it would be a valid approach for an institution that hosts a research data repository (in this case, Dataverse) to create a “publish” feature that would push datasets into Omeka S (or an Omeka S plugin that would collect the published datasets). Files hosting would be shared between the two systems.
This is to avoid duplicating resources between data management and data publication tools.
If some of these research data are quantitative (economic, demographic data), do you think it would be relevant to also use Omeka-S to publish and highlight them (by adding javascript data visualization libraries to front-end) ?

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.