You already note the issue with identifying that the question exists - there is no good mechanical method for this. If someone wants to find out if a specific question has already been asked, a cursory search on their part is going to be far more successful than waiting for people on the site to realize that someone may have proposed it back on Area 51. So let's focus on what happens when the question "does not exist", which provides two primary issues.
One, if the question already does exist but simply hasn't been linked with Area 51, then a new user will end up posting a duplicate. This is worse if the original question may have been closed and/or deleted, so there is a lot of potential for a very unfriendly experience.
More importantly, the questions in the definition phase only serve as a basis of definition, and do not necessarily reflect the direction that the site will actually grow, and especially not how the site may currently be at the time of clicking. Sometimes a question looks like a great idea when you are voting in the definition phase, but when you try it out in the actual beta it turns out to be a horrible idea that sets a bad precedent for the remaining days in the beta. Adding this system gives a false sense that questions from the definition phase are definitively appropriate for the site when in reality they're simply an initial guideline.