Verizon Note 3 CyanogenMod Question

[802skier]

I have a Verizon note 3 running the OTA NC4 4.4.2 kernel. When I tried to flash TWRP, a message came up stating, "Software unauthorized by Verizon has been found on your device." I had to factory reset. Using safestrap, I tried to flash CyanogenMod in ROM slot 1. It loaded into a never ending black screen.

My questions are:

1. If I get the bootloader unlocked (which I will be doing), can I install Team Win without a problem?

2. If I can get TWRP, will CyanogenMod work on my phone?