[y7]

Yes, all existing FHE schemes have this property (called semantic security). The encryption algorithm is a randomized algorithm, which takes the plaintext and a random value as input (just like an IV). Note that we're talking about public-key crypto here, which is a different primitive from the symmetric crypto you're thinking of. Each key is actually a key pair consisting of a secret key and a public key. Such cryptosystems are based on some mathematical trapdoor: only with the secret key are you able to "undo" the randomization and learn the plaintext. It therefore doesn't matter if you want to undo the randomization on a direct encryption of a plaintext, or whether the ciphertext is the sum of several ciphertexts.

If you want to see how this works on a bit more technical level, look at the ElGamal cryptosystem [1]. It is in fact partially homomorphic (you can add ciphertexts, but cannot multiply), and it's probably the easiest to understand system with this property.

https://en.wikipedia.org/wiki/ElGamal_encryption