It may be useful to define what is meant by noise. Noise is data that is selected randomly from some distribution. @Thomas deals with comparing to random bitstrings (where each bit is equally likely 0 or 1) and notes that because not all bitstrings of an appropriate length are possible values in most asymmetric encryption functions, real ciphertexts will be distinguishable from randomly generated bitstrings.
A different approach to defining noise might be to take the set of all valid values in the encryptions scheme and randomly choose one of them (with equal probability). For example, pick a random integer in [0,n-1] for RSA, a random point on the curve for Elgamal on elliptic curves, a random number in subgroup Gq for Elgamal over the integers, etc. For these distributions, we can ask, is an actual ciphertext distinguishable from a randomly chosen but plausible value for a ciphertext?
If you are given a ciphertext only (with zero information about the plaintext), then both RSA and ELgamal are indistinguishable from a randomly chosen but plausible value. However if you are given a plaintext and either its corresponding ciphertext or a random plausible value (and you need to decide which), then things are more interesting.
Textbook RSA (e.g., RSA without padding) is distinguishable from a random plausible value. This is for two reasons: (1) RSA is deterministic, meaning it is simple to encrypt the plaintext and see if it matches and (2) RSA leaks one bit of information about the plaintext.
Textbook Elgamal (e.g., Elgamal as originally proposed over the integers mod p) resolves the first issue with RSA. It is a randomized encryption algorithm meaning if you encrypt the same plaintext twice, you get different, indistinguishable results. However it does not resolve the second issue and still leaks one bit of information about the ciphertext (whether it is a quadratic residue or not).
Elgamal and RSA-OAEP both resolve the shorting-comings of their respective textbook versions. Textbook Elgamal is already randomized, so it is simply a matter of using it in a proper setting (in this case a subgroup of the integers between 1 and p-1 where they all have the same value for the leaked bit, or such a group on an elliptic curve). For RSA, padding adds both randomness and destroys the correspondence between the plaintext and ciphertext that is leaked in its textbook version. For both of these encryption methods, a ciphertext is indistinguishable from a random plausible ciphertext, even when given the corresponding plaintext.