I tried this for the first time last year. That same video is what got me started. Worked very well and I'm about to tap into my stash for this year. My takeaways:
I had about a 90% success rate which another video indicated is pretty typical. A percentage of eggs will either leak out or have a crack, allowing the the lime-water in and spoiling the egg. They are generally obvious, but if you have any doubts, crack the egg into a cup to check it before using.
The white/yolk are a little softer than fresh. I had a hard time making easy over eggs. They tended to be better for scrambled eggs. The eggs tasted fine- no lime taste.
I store eggs when the girls are laying most heavily in the spring and they carry me through the winter when they pretty much stop.
I can see why old-time homesteaders used this technique. It works pretty well with no refrigeration. A good alternate would be to freeze scrambled eggs if you have the freezer space.