No, sorry my analogy was lacking. The complete act of rolling the two dice and covering them is analogous to entanglement. When you check the entangled particle, you collapse it from a non-precise superstate into a classical state. That means that if Person A takes a measurement on the superstate die, they'll collapse the waveform into a classical die with the measurement of 2. If Person B then reads their die, they'll also get a classical measurement of 2. There is no way for Person A to effect the die in such a way as to give any classical information to Person B. Neither person can force the die to fall in a certain way as the die is rolled, nor can either person tell in which way they caused the die's waveform to collapse. Once the waveforms have collapsed you have to be in the same local space to set up entanglement again. You can add information into the initial setup, but the particles still have to move from the local system at the speed of light to transmit said information.

The reason all of this is notable at all is because quantum superstates are(usually) non-deterministic. If we tried to make the analogy as accurate as possible, the dice would continue spinning in air under the cups until one of them was revealed, then that die would stop spinning and show a number, the other die would continue spinning until it was revealed and somehow show the same result even though no communication happened between them.

Wikipedia's article on the no-communication theorem gives what is probably a more accurate analogy:

In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listensers to use their radio receiver to send messages to the other listener. This analogy is imprecise, because quantum entanglement suggests that perhaps a message could have been conveyed; the theorem replies 'no, this is not possible'.

The basic reasoning behind why it's almost entirely likely that it's completely impossible for FTL communications is because when you boil it down all information transfer is a state change, and any classical state change requires energy. If you could move energy ftl you could move matter ftl and then you'd start having paradoxes and problems all over.