VZW OTA, right? Well, as per the XDA page in question, I'm supposed to taunt you for not reading the red large writing, but the page says clearly, twice, that 'using this WILL NOT set the "Knox Warranty Void" flag.' It sets the "custom" flag; don't worry about that now. Later on,
Resetting the "Custom" and open padlock indication during boot can be worked around using the Xposed Framwork and Wanam Xposed. Get those two from the Play Store. In Wanam, tick "Security Hacks", "Fake System Status".
So you're not unlocking that phone any further than it already is; and you're not installing a custom recovery. You can install Safestrap recovery (unless you have encryption enabled; SS will bootloop if encryption is enabled). SS is a modified TWRP for your rooted-but-unlocked S3; that's the only recovery we OTA Jellybean users have got right now.
Note: you can only use ROMs based on 4.3 modified for a rooted but locked SGS3 (there are a few). Any ROM you install with SS is going to sit on top of the stock ROM that we can't (yet) get access to, and all of that goes in internal memory, so keep ROM size in mind when shopping ROMs.
Last thing: before Safestrap, if you want wifi, you need to flash the kernel modules. All that info is in the SS thread which I highly suggest reading. (I can only post 2 links since I'm new here; I chose carefully, but please read the SS page.)