I don't see 'Invisible" status in Nokia IM. Is this feature available? Or do you have a timeline as to when it will be developed and made available for Nokia phones? I am using E7 and sorry to say that this status is made available in APPS like Nimbuzz! This should be a simple coding change as you use xmpp for nokia IM.
Honestly phone information does not even matter here. Use any phone, download Nokia IM from Stores and see if you can set "Invisible" status while logging on to GTalk. This feature is available in Nimbuzz, very surprisingly Nokia Developers are yet to learn how to code this.