Well, sure, except you know that Gallup is never going to release a poll that says, "Clinton Choice of Ignorant," nor would the Times, etc print it nor CBS, etc broadcast it.
I have often wondered about the point you raise, though. Are they any polling orgs, or any circumstances, where qualifying questions are asked to measure the relevant knowledge of respondents?
They have targeted surveys, most often used in Market Research, that 'Qualify' respondents. This technique is used often whereas this type of survey is just for publicity or to prove a pointless point IMO.