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Since magnetic coil vibrates in speaker it should also be producing EM waves.

So if we put a speaker in vacuum chamber we wouldn't hear anything but is it possible to detect EM waves produced by the coil from outside of the vacuum chamber and convert them again to Sound Waves?

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Irrespective of the inner workings of any speaker, this is what is usually done in any such situation! Think of how astronauts aboard the ISS communicate with the earth. Even if they were to shout at the top of their voices we would not be able to hear.

So, they transmit via EM signals (radio waves to be precise) which are converted back to voice back on earth.

Thus, in order to overcome the problem of sound waves not travelling through vacuum, it is possible to transmit it via other forms and that it what is done presently.

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