having absloutely no ECs would reflect very badly on your record. i applied to pritzker's early application process, and i got some feedbacks as far as why my application was not successful despite a strong academic record. i had two or three ECs, and no significant clincial experiences. they rejected me first round. if you were a borderline applicant, your ECs could determine whether you get into medical school at all. if your numbers are really great, it could determine whether you'd get into a top program. regardless, absloutely having no ECs, or having very little ECs shows that the applicant has neither the incentive nor the ability to handle a variety of tasks at the same time.
think along the more intuitive lines, do you think that all the admissions officials are going to read through your thousand word essays? with your numbers, the next easiest thing to look at would be the table of extracurriculars. if everyone else has a very impressive list while yours is empty, how do you think that's going to look? this is also the reason why on a resume, for instance, when you are trying to find a job, the most important part is the work experience, not education/GPA, which is usually placed at last.