There's no doubt that interviewing early will give you a higher chance of acceptance due to more open spots in the class. Given that, it also depends on your application as a whole. If you are a high-end applicant who is interviewing late due to personal reasons or submitting an application late, you will still have a decent chance of acceptance, whereas if you are an average applicant, you will be in a tougher spot than a similar applicant who interviewed earlier.
I suggest that you trust in yourself and your application, give a great presentation of yourself, and leave the rest to the adcom. If you are a worthy candidate, you will definitely have a chance of acceptance.