I have read several articles pertaining to rooting a Note 3 and voiding it's warranty. I know a custom rom, or custom rom app would change the binary counter. Would I be safe rooting and using Titanium backup or similar to remove / freeze samsung bloatware?
No in fact there's the
Knox void warranty flag that will be set to
0x1 if you are on the 4.3.
Knox is not yet really understanded but so far something is sure, if you flash any rom that does not contains the knox security (official or not official) it will void your warranty.
So even if you flash a 4.2.2 version of stock rom from samsung it will set the knox void warranty to 0x1 and your phone will not be supported by Samsung.
Edit 1 : Well according to comment, it might be possible to avoid the change of th knox flag, with the root method from root de la vega. But still if you are in USA (where voiding warranty with a simple logical flag is possible) be carefull while proceding because it still tricky.