Actually, not quite. For the analogy to work, each half of the coin is equally heads and tails until the measurement. Only the entanglement itself (i.e. that one is opposite the other) was encoded in the envelope to begin with.
We might need another analogy. Consider Donald Trump and Hillary Clinton as entangled particles guaranteed to hold opposite views on any given topic. With Hillary in New York and Donald in Los Angeles, ask Donald a question about one of the few things he has no opinion on. Until you ask, nobody (including Donald and Hillary) can know what his answer will be. But as soon as you ask and he answers, we Know what Hillary thinks about the subject as well.
Now, at this point, Donald and Hillary have taken Stands on the issue. Before the question was asked, each of them equally supported and opposed the issue. Once the question was asked, one fully supported and the other fully opposed the issue. If you then manage to convince Donald to change his mind, your efforts destroy the entanglement, so it will not change Hillary's opinion.