I can access the Web Store fine with my apps account. The apps account administrator needs to enable it in the Apps control panel. IIRC it's in "Organisation and Users" --> "Services".
The only thing not in there (that I've found) is Google+/Profiles.
Chrome Web Store is not available for .com. Learn more about Google products you can use with @*.com."
I can't even view a Chrome extension since I'm a user of Google Apps.