I used Google Voice (GVoice) for a long time prior to Note 3. Voicemails to my Gvoice number will go to Gvoice, not T-Mobile or AT&T (previous carrier). Voicemails to my phine number will go to the carrier's.
With the Note 3, Voicemails for my GVoice goes to. .. the carrier's?
1. Someone call my GVoice number and left a message
2. GVoice indicate there's a Voicemail.
3. T-Mobile ALSO indicate there is a Voicemail - icon on notification bar.
I can even press and holds "1" in the keypad and dial to T-Mobile voicemail systemand listen to the message.
I already setup GVoice as shown in screen shot.