What I will say below is obvious, but it is how applications are evaluated here:
If you relevant work experience, your application is stronger in that area.
Otherwise, you will have to be comparatively stronger in other areas, to compensate the initial lack of work experience. The summer internship will give some practical experience.
As Eugene's example shows, if you are strong in other areas and successful in the program, you should be able to start a career in quant finance upon graduation even if you come into the program straight from college.