I'm not sure in the US, but trade in dead coral is very restricted in Europe. There was a time when people simply smashed live corals up, bleached them, and sold them as curios. This was obviously a disaster as far the coral reef ecosystem went. I would be extremely skeptical of any trader telling me that the corals were "collected after they had died naturally". I simply don't put any faith in human beings when it comes being honest about this sort of thing when cheating is so easy and so profitable.
There's nothing to stop you using bits of dead coral you have found on holidays, any more than using sea shells, and both can be used freely in fish tanks. Coral is made of aragonite, which is a form of calcium carbonate slightly different to the calcite in things like oysters but identical to that in marine snails and clams. It is totally non toxic, though as you say, it will dissolve gradually, raising the pH and hardness. Some fish object to this, as you probably realise. But hard water fish, like guppies and mollies, will be fine.
Equally, you could use fake corals. This do not affect the pH or hardness, and so could be used freely with soft or hard water fish. In a 10 gallon tank this might be rather fun: a swarm of neons around a purple or green fake coral would be rather something!
Cheers,
Neale
