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Suppose I run a fully homomorphic encryption scheme (FHE) on a cipher text c, generated by running AES on plain text m and get c' as the output.

What would the output be if decryption of AES is run on c'? Would the decryption of c' using AES key result in a cipher text that decrypts to m if the decryption function of the FHE was applied?

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No, this won't happen. You can't change the order of operations. For that to happen, you'd have to homomorphically compute the decryption function of AES on the encrypted ciphertext c'.

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