Yes, after some testing I can confirm prompts while working with AD Kerberos + SSO are avoidable using IE 10, Firefox and Chrome.
I have configured this in alfresco running in a Windows 2008 computer (pending to try in a Ubuntu computer).
I followed the Alfresco One 4.2.0 admin guide and I must say the only thing I missed is any reference to the authentication chain kerberos in the Kerberos section.
And be careful! Usernames, spn, paths, etc are case sensitive!