The answer is no… Admissions committees will not be more impressed with one school over another. You will get into grad school for biology by maintaining a high GPA, doing well on the GRE, getting to know your professors so that they can write you personalized letters of rec, doing research, etc.
My daughter has an internship this summer in the sciences at a very well known facility. There are about 50 students from a variety of schools: UNC, Duke, Harvard, Cornell, Clemson, U Mississippi, Kentucky, Clemson, etc.
It’s what you do …not where you go. You also seem to be underestimating the strength of the programs at UNC.