There are some pretty big organisations that use Google Apps. For example, BSkyB use gmail for customer email accounts, and the University of Cambridge and the University of Sheffield both use Google Apps to some degree for staff/students.
There's a local tech college that uses it for email as well. But that does very little to shake IE's hold in the enterprise. Providing customer or student email is one thing, migrating your staffs away from an MS Office workflow (especially for academics, who's job is publishing), is something wholly different.
I'm not saying that businesses don't use web apps, but counting on web apps to shake IE's dominance in enterprise, at least in the short term, is wishful thinking.
