Unity Webapps work in Firefox and Chromium, and they could be made to work in other browsers as well. There's a library that encapsulates most of the code to write an extension.
Chromium that you can download from everywhere will find the extension and load it. So you'll get basic webapp integration. There's a patch, that adds the ability to manipulate the list of integrated sites, but everything else will work without that patch.
Chrome will not find the extension.
The patch for laoding extensions off the filesystem was merged upstream in Chromium an is in the latest release of Chrome, but it looks in a different path than where the extension is installed.
If you would install the extension where Chrome would look at it should work. But webapps are not tested with Chrome.
The answer was given in following "Ubuntu on Air" hangout: https://www.youtube.com/watch?feature=player_detailpage&v=6K_n8DtDl2k#t=42m42s
The above is basically a transscript of the Answers by Robert Carr and Ken VanDine (Ubuntu Webapps Team)
You should have know where the answer was to be found: at Time: 42m42s ;-)