I'm interested in adding it to my own LinkedIn profile, not my institution's page. My institution is not a member of GovLoop--I am as an individual--so it wouldn't be appropriate on our site.
I actually DON'T think it belongs out there as part of the agency's public face, unless the goal is to get a lot of citizens joining GovLoop to watch us talk. For me, that would dilute the value of a social network for public employees.
Gov-to-gov is different, and it does make sense on pages that operate within that context, but not an entire web site with a public face.
Individuals blogging about government might want it as well.