Now I'm trying to do the same thing on the desktop version of Outlook, but I get an error when I do "check name" and I can't continue. It is possible to workaround that?
Outlook cannot set up an account that uses ActiveSync, it can only speak the native Exchange protocol through RPC (or RPC over HTTPS, also known as Outlook Anywhere).
Gmail only publishes an ActiveSync endpoint, so unfortunately on the desktop you'll need to use IMAP for email and Google Calendar Sync for calendars.
It appears that Outlook 2007 has proper support for calendars over WebDAV, so you might give that a try. You still won't be using the Exchange protocol, but at least you won't need a program sitting around just to sync calendars.
Just saw that according to the Microsoft website, Outlook 2013 will offer this feature.
Exchange ActiveSync Support Connect Outlook with Exchange ActiveSync, and you’ll receive push-based email, appointments, and contacts via the most popular email servers and services.