Yes the web dashboard app will become part of ArcGIS online, and once users sign in to their organization, they will be able to open a single-display operations view in the web dashboard app. It's a HTML viewer so there is no need to deploy or install dashboard software.
For the first release, although we don't have a detailed date set yet, we are looking at Q1 2014. Most likely around Dev Summit time frame (somewhere around March/April).
We would love to know if you have any specific requirements or comments on the web edition of the dashboard app.
Thanks
-Jay