I'm not exactly sure what you mean, "try the extension" but if you mean are US and EU sites separate instances, yes they are. They are kept entirely separate and no user data (or any other data) is stored. This is for data legislation purposes.
When I click on the extension icon and complete my log in details I get this message
Unable to retrieve access token.
Please check your username and password are correct and retry
Not sure what I have done wrong.