I'm confused why you want/need to do this since you can already access Google Calendar in the cloud, and set it up on your iPhone/iPad/iCal without using iCloud.
Also "iCloud accounts" and "iTunes accounts" are the same thing. If you have 2 usernames and passwords, you have 2 accounts (Apple IDs).
I see in my email that I have recieved a "Please verify the contact email address for your Apple ID" email from Apple in the past, although I didn't seem to get one when I created my recent account that I used for iCloud. Did you check your junk mail?