Boiling is usually done with driftwood, to remove certain chemicals in the wood, known as tannins. Coral has no tannins, and so, there is no need to boil it, unless you fear that a saltwater disease might get from this dried out coral, into your tank, and survive long enough to infect your freshwater fish. That's not likely either.
Testing is done with rocks, if you don't know what they are. You use a bit of vinegar, and either put part, or all of the rock into that for a while (reccomended) or pour a bit of the vinegar on the rock (not so easy to tell) If bubbles come off the rock, it is a sign that the rock contains lime (calcium carbonate) which will slowly leach into aquarium water, making it harder, causing lime buildup lines on the sides, and killing some fish.
Fortunately, we know what coral is made of, and do not need to test it. Coral is made from calcium carbonate. It should make bubbles if left in vinegar.
Ouch... Well, let's not get too discouraged yet. What kind of fish are you hoping to keep? See, some aquariums can be run just fine with lime-containing rocks in them. In fact, it's good for some fish.
Most cichlids, for example, come from african lakes that have naturally hard water, and for them, a little hardness leaking out of a bit of coral is just fine.
Guppies, golfish, mollies, and most other livebearing fish can survive in such a wide range of conditions that putting them in a hardwater tank will rarely kill any of them.
So really, it's only fish from places like asia, and south america, where the water is usually very soft that hard water becomes a real threat.
For example, you wouldn't decorate a discus tank with that piece of coral, and most tetras wouldn't like it much, although a number of them might survive.
If you plan on keeping a hard water tank, you can just throw the piece of coral in right now. If you plan on keeping a soft water tank, it's not so good, but, of you are dead set on using this piece of coral, there is one thing you might be able to do.
Some pet stores sell types of epoxy resin, which you can either dip the coral into, or spray the resin onto the coral. Once the coral is TOTALLY covered in this stuff, the calcium carbonate it is made of will not be touching the water, and therefore, will not dissolve slowly into it.
It's hard to find this sort of resin stuff these days, and unless you've got a monstrous large pet store, you may have to find an online source.