From my experience, colleges evaluate every application individually. If the student has what the college is looking for, he is in. The high school name does not mean much excluding the top IVY League feeding private schools in New England area.
Here, I assume you are thinking of American colleges. I have a son in college. The high school he went to is just an average school in the States. However, one or two outstanding students always get accepted to the top colleges every year. If SMIC does not offer enough courses, you always can take online courses from American colleges such as Standford EPGY or others which offer online independent study courses from high schoolers.
FYI, the most important thing for college application is how you present the total package. A good counselor plays a very important role. Of course, the parent can be an excellent counselor as long as you have time to do the search and understand your child well. Anyway, this is my 2 cents from playing the counselor’s role for my son.
Thanks for everyone. I have learned a lot from this forum. My family will move to Shanghai next spring/summer. I am searching schools for my middle school child now.