No, it wouldn't be good for faster than light communication. But it could be used for secure communication, or implementing a "shift" register in a quantum computer. The separate line of communication doesn't pass information about the initial state of A, just its final measurement, which actually says nothing about it's initial state to anyone or anything except ion B. And, because we're talking about quantum mechanics, A's initial quantum state could be a superposition of states, not just "0" or "1".
Let's see if I can shorten my explanation to this: All the second line of communication says: "Entanglement between A and B was successful. Please use method 1 (or 2) to set B to A's initial state."
I hate to contradict a good rant, but in actuality, this "teleportation" can be used for communication.
Here's the experiment, without all the theory:
1. Put the atom A into the state you want to teleport to B. Let's call the two states "red" or "blue". Put atom B into a "known" state.
2. "Stimulate" both atoms so they will fire off a photon. The photon from each will either be a "red" type or "blue" type, but we won't know which (that's important).
3. Both photons "meet" in a beam splitter, then go to separate detectors.
4. If one detector detects a "red" and the other a "blue", then continue, Otherwise go back to step 1. Key here is that this step "confirms" the atoms are now entangled. At this point, if we measured A, the result would determine the B measurement. But we're not going to do that yet.
5. Instead, apply an operation to atom A, so that subsequently measuring it doesn't lock B into a "single" state. It instead puts it into one of two states, still dependent on the initial state of A.
6. Measure A. The measurement will either be "red" or "blue".
7. Use the measurement of A to choose the final operation to apply to B. B will, due to the magic of Quantum Mechanical entanglement, now be in A's initial state, whatever that was.
If A was initially in a "red" state, then measuring B will get you "red". If it was original in the "blue" state, measuring B will get you "blue".
While this does require that you repeat until you get a "red/blue" detection and you need the final A measurement to know what operatation to apply to B, the final A measurement doesn't contain the information about its original state. You could do the final operations on B only when you received the "red/blue" at the detectors and "red" measurements of A. B will still end up in whatever state A started out in.
So, to summarize one last time:
Apply operations to ions A and B. They fire off photons simultaneously into a beam splitter and detector. If the photon detectors detects a particular condition, then operate on A and measure it. Depending on the A measurement, apply one of two operations on B. B will now be in A's original state. If A started in a "singlet" state, then in the end B will be in that "singlet" state, and measuring it will indicate what that state was.
That seems like communication from A to B to me.