I can tell you on my Samsung Galaxy S-III, HTC EVO LTE and Motorola Photon Q LTE, I do not see any difference in battery life in CDMA/LTE mode versus CDMA only. I do see a slight difference on the Galaxy Nexus and a pretty noticeable difference on the LG Viper.
I would think LTE will make little to no difference on the Note 2.
Robert via Nexus 7 using Forum Runner