[Q] Simple Question (hopefully) for the HTC One M7 Verizon topic

Ok, so I have been searching for two days for information on whether or not you can gain root access via SU or SuperSU if you are running 4.4.2?

I AM NOT LOOKING FOR AN EXPLOIT TO UNLOCK AND GET S-OFF! (I'm not yelling, just want to make sure that this is understood)

I already have my bootloader unlocked, S-OFF, and a custom recovery installed (CWM), but every-time I install the .ZIP file for SU in recovery and then go to it after phone is rebooted (again on Stock KitKat 4.4.2) it still says the SU binary is out of date or unavailable. If I try to open a ROOT Access only app, it warns me the device is not rooted and closes.

My fastboot/adb are working fine from my PC for flashing and getting into fastboot oem rebootRUU mode. Just in case it helps anyone with an answer is are the details of my getvar all:

(bootloader) version: 0.5
(bootloader) version-bootloader: 1.56.0000
(bootloader) version-baseband: 1.13.41.0109_2
(bootloader) version-cpld: None
(bootloader) version-microp: None
(bootloader) version-main: 3.11.605.1
(bootloader) version-misc: PVT SHIP S-OFF
(bootloader) serialno:
(bootloader) imei:
(bootloader) meid:
(bootloader) product: m7_wlv
(bootloader) platform: HBOOT-8064
(bootloader) modelid: PN0731000
(bootloader) cidnum: VZW__001
(bootloader) battery-status: good
(bootloader) battery-voltage: 4293mV
(bootloader) partition-layout: Generic
(bootloader) security: off
(bootloader) build-mode: SHIP
(bootloader) boot-mode: FASTBOOT
(bootloader) commitno-bootloader: dirty-4dab9d12
(bootloader) hbootpreupdate: 11
(bootloader) gencheckpt: 0

I have no problems changing my CID to SuperCID and back to the Verizon variant.

In the most basic way I think my question can be asked is this:
Is it possible to achieve root functions with a Stock ROM running (KitKat), if you already have an unlocked bootloader, and S-OFF?

If not, the reason I still have the STOCK ROM on my HTC One (m7) is because I haven't found a custom ROM that's supposed to be really stable, that I like as of yet, and so was hoping to just run stock until some more dev. goes on.

Thank you, Thank you, for your help in advance!!

PS: If it's possible to flash SU using Terminal Emulator app while phone is on and running KitKat, could you please also direct me to where I would find those commands? Thanks!