For example, if I go to UMichigan for Undergrad CS, would it benefit me in any way to gain admission to its grad school?
It’s common to switch schools for grad school, but it completely depends on what you’re doing. I know you’re majoring in CS - why do you want to go to grad school?
Some universities have combined BS/MS programs these days and that requires you to stay at the same school of course. However, as @PengPhils notes, you might not really need to get a MS right away. Start with the BS and then decide what is best for your career in your third year. By then you wil know if the kind of job you want requires graduate school. Generally for CS, that is not the case.