<p>You could say that you are busy when they suggest a time to meet. But, they might end up suggesting another time. Otherwise, I don't know how it effects your chances. Dartmouth doesn't care about showing interest (as someone else said, you show interest by applying).</p>
<p>Also, Dartmouth doesn't need to be one of your top choices for it to make sense to go to a 45 minute interview. What if you don't get into your other choices?</p>