Those clutches only engage when there is enough bias. I don't think 6% is enough to engage them, but maybe someone else knows better. Beside that, I was really trying address the OP's concern, because I wasn't clear if he or she had a locker/lsd and even had to worry about it.
For the rest of us, it's just a talking point. Myself, I wouldn't worry much if I had an open diff or lsd. But, someone more in the know could certainly explain the damage that could be expected with a lsd or open diff.
I would check with the manufacturer of any given unit. At one time, before Eaton bought Detroit, I was told by a Detroit engineer that the True Trac (as an example) only transferred "up to" 30% to the wheel with traction, meaning there was plenty of "slip" still at the other wheel (which 6% wouldn't be an issue). Also, tire sizes are not equal. A semi-worn 35" may be 34" and a stock 33" would then be much closer in size. If you've got lockers front and rear you're probably still not going to do much mechanical damage, my opinion is that the tire is more likely to wear funny than damage a quality locker.
Running the stock size only until you can get the 35" repaired or replaced shouldn't mean running it very long.