Proving an encrypted message contains (but does not 100% consist of) a plain-text message?
A fundamental theorem of cryptography (Goldreich, Micali and Wigderson 1986) states that any NP statement can be proven in zero knowledge. So, the answer is yes. For any polynomial-time combination of $X$ and $Y$ into $Z$, it is possible to prove that $Q$ contains $X$ in zero knowledge. 

Note that the general zero knowledge will not be practically efficient since it requires a Karp reduction. However, depending on the combination and the public-key scheme, it may be possible to do this very efficiently. El Gamal specifically is very amenable to efficient zero knowledge, but it depends on the combination you mean.