what cam30era said.
If you want a full custom ROM that only functions correctly by using a custom kernel, you will need to buy a developer edition Note 3, not a retail device. This is a consequence of the fact that the VZW retail Note 3 has security protections that (have not been circumvented at this time and) prevent the booting of custom kernels.
It is my understanding that CM11 needs kernel features that are not present in the retail, stock (MI9, MJ7, or MJE) kernels. Whether this causes bootloops, UI framework crashes, or something more minor (loss of some functionality) I don't know.
My guess is there will be little motivation for CM11 to "officially" add the VZW Note 3 as long as it's secure boot locks remain un-hacked, as there aren't many dev-ed owners.
[OFFICIAL] CyanogenMod for DEVED VZW Note 3 (HLTEVZW) [2014-01-11]
"I'm gonna start coding placebo apps. That way I will be sure that the complaints are real and the praises hollow."