SRWare Iron is said to be more privacy-minded than the ordinary Google Chrome browser, but it still makes several (mostly encrypted) connections to Google. According to the Fiddler Web Debugger, Iron33 contacted the following hosts just from being started:

CODE
plus.google.com
http://clients2.google.com/service/update2
www.gstatic.com
ssl.gstatic.com

(I don't use Google Plus. Some sites say clients2.google.com is for browser extension update checks, but I don't have any extensions installed in Iron.)

Next I upgraded to Iron34. On its first run it started Windows' Background Intelligent Transfer Service (User-Agent: Microsoft BITS/7.0), which among other things contacted:

CODE
cache.pack.google.com
****.c.pack.google.com (URL edited by me)
clients2.google.com

--possibly downloading 500KB or more.

Iron34 itself often also contacts

CODE
translate.googleapis.com

I have no idea why all these Google connections are done, or if/how they violate the user's privacy, but my other browsers make much fewer (or no) third party connections, and when it happens they're usually related to extension update checks or cryptographic certificates (the latter are done by Iron as well, but I've excluded them above).