Yes, with most operating modes of AES, the length of the encrypted string is the same for everyregardless of key size (128, 192 or 256 bits).
That's because AES-128, AES-192 and AES-256 all are 128-bit block ciphers, meaning they operate on 128-bit data blocks, regardless of key size. The key determines the mapping of 128-bit plaintext blocks to 128-bit ciphertext block, but the key size is independent of the block size.