Documentation is a "gimmick" in this hobby. If you bought it straight from Atlantis corals, the only documentation you would get would be your receipt, so like everyone is stating, what you're really looking for is what is called lineage. What that would look like would be something like this. I have a Tyree pink lemonade that was purchased from Aquaworld in PA. They got it direct from Tyree. If I can tell you something like that, then that's considered lineage. Usually for it to count for something though, they need to be bought from a larger presence. Therefore selling my pink lemonade that you bought from me wouldn't really qualify as having "lineage" because cloakerpoked isn't a household name, and while everyone in the Pittsburgh area knows me, I'm willing to bet there might be 1 person in all of the US away from this city that would recognize me.
You would however, know that it was a tyree, or at least that I was dumb enough to buy it as a tyree

If I were you, I'd stick to buying from reputable people who take good pictures of their stuff, or even better for you, something that you can see personally. Names are helpful to ID things, and important if you are selling such things, but Tyree also takes things that are in common circulation before hand, "brands" them, and then sells them for 2-5x more than the current going rate is. That's just crazy, and in that case, you're better off just buying a non-tyree coral (see....Pink Elephant Palys).
As far as chalices are concerned, you're unlikely to ever make back a ton. With anything, if it grows big enough, you'll get your money back and then some, even the $15 birdsnest frag you got from someone local. Chalices generally grow slower, but as they are popular for longer, and fragged by a lot of people, market conditions depress pricing very quickly. So that frag you paid $300 per eye for is now going for $50 per eye by the time you can frag 2 eyes off it because there are hundreds of other people trying to sell the same thing. You'll still eventually make your money back, but no quicker than anything else.
The bottom line for me would be to suggest that you not look at the Tyree name, and look instead for reputable sellers with very detailed pictures. That should be a better indication of what you're getting than getting hung up on what they're calling it.