If it does, it matters very little. Some medical schools will say they give little preference to undergraduate college and others say they give no preference. Of course it is more impressive for a student to have a 4.0 from Harvard then a 4.0 from a small town college, but generally, where you attend undergrad does not largely affect medical school admissions.
Regardless of your college choice, GPA (overall and science) and MCAT score are the two most important factors. Medical schools will almost always take a student from a small college with a high GPA over a student from an Ivy League with a low GPA.
As a pre-med, you should not think too much about the college you attend, but how you do at the college that you chose.