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Hi, I'm Mike G and I'll be assisting you. In most areas, yes. A cord set to a receptacle is an alternative.
MC cable having a ground wire would be much better than BX. It only has a foil for a ground.
Not a Romex a cord set. Sold complete with a plug on it.
Like I said, it is permissable in some jurisdictions, but not all. The MC would pass everywhere. A cord set would also pass.
Good choice. You're welcome.