As to your question, "why would you ever bother to preach the gospel to the unbelievers?"
There are a number of reasons why. One is because I am at times led by the Holy Spirit to preach to unbelievers.
Why in the world would the Holy Spirit lead you to preach to an unbeliever, when by definition of Reformed Theology and your theology, the unbeliever is wholly and completely incapable of understanding a thing of what you are preaching.
Ask Him if you will. I just gave you my honest answer. Would you want me not to obey the Holy Spirit when HE leads me to preach to people? Even if you do want me, I would listen to the Holy Spirit's voice, not yours.
So, you are saying that the definition of Reformed Theology, the unbeliever is wholly and completely incapable of understanding a thing of what is preached to him. So what? I care less of the definition of Reformed Theology or what have you.
All people started out as unbelievers. You and I, all Christians have a point in their life when they believed. As such, all started out as unbelievers. Now, among unbelievers, are the elect. They are those who will, in time, become believers. I was once an unbeliever until I became a believer. I wasn't born a believer, were you?
Also, if you can't, in a few moments of speaking to the person, know whether they are believers or unbelievers then obviously you are not asking the right questions.
If, after talking to them, they profess to be believers, then I would know. And if they are, I really need not preach the gospel, would I?