Can I completely wipe a Galaxy Nexus
Yes you can. 

Actually, wiping an (unrooted) Android device is relatively easy. Just go into Settings and look for Backup &amp; reset option. At the very bottom of the options you'll see Factory data reset, hit it and you'll see some confirmation dialog, go through that and your "new" Galaxy Nexus will be ready in a couple of minutes ;)

This method will compeletly erase anything stored on the phone's internal storage, including all Google-related data.

Note that it's a good practice to also erase the sdcard partition alongside the process. Some Android application uses the sdcard partition to store user data which might be restored even after you wiped the device.

Good luck! :)