No, If we assume that the mythical computer can brute force the multiple AES encryptions and there are many ciphertexts available which are encrypted under the same key and their corresponding plaintext are not random.
The brute-force code can keep track of the meaningful plaintexts for each ciphertext and finally can perform an intersection of possible key candidates to find the key.
Yes, If the plaintexts don't contain any meaningful information to distinguish them from random than there will be no possibility. So at least a distinguisher is required.