After some trial & error, root has been obtained for the VZW Galaxy Note 2 - this is just root, the bootloader is still locked...
This is a copy / paste from droidstyle's post on the XDA Forums ( [GUIDE][VZW Edition]How to Root the VZW Galaxy Note II and more! - xda-developers )...
Standard Disclaimer Applies....DroidForums.net, XDADevelopers, nor anyone associated with this method is responsible for any issues that might arise from this method - you are using at your own risk and assuming the liability & that you understand what you are doing.
Section 1: How to Root Stock JellyBean with Odin - VZW Edition only!
Step 1: Download and install these files to your pc:
Step 2: Download one of the rooted stock odin images below to your pc:
Root66_VZW_stock_VRLJB- Dev-Host - root66_VZW_stock_system.7z - The Ultimate Free File Hosting / File Sharing Service
Step 3: Power device off, hold the volume down/home/power keys until you see a yellow triangle, then press the volume up key to access "odin or download mode".
Step 4: Open odin and connect the oem usb cable from pc to device. Adb driver should automatically install(atleast it did for me on windows 7). There should be a "comport number" in upper left hand corner of odin indicating communication between the pc & device.
Step 5: Uncheck Auto reboot
Step 6: Click on the PDA function of odin. Select the rooted system.img you downloaded in step 2, then select start. This operation should take less than 8 minutes before odin will say pass/reset.
Step 7: Pull and reinstall battery.
Step 8: Press and hold the volume up/home/power buttons until you see a green android. You should boot into ASR(Android Stock Recovery)
Step 9: Wipe cache.(If you experience errors, boot back into ASR and wipe data.)
Step 10 reboot!
*Everything is working folks!! We now have a solid root method!!!
Credit goes to MrRobinson and Beanstown101!!