I checked the analytics dashboard yesterday and updated the website: the only data that I'm not getting though is the users country/city and their provider. So in a sense it's better for your privacy: the IP is not your own!

I'm not an expert of Analytics but I'm also assuming that since the cookies are different (because the HTTP call to analytics happens on a different domain than usual) it shouldn't be able to track you just as well: G Analytics don't know your IP and have no trace of your previous anonymous IDs set in your cookies!