ALL schools like it when you are paying for the education. This can be Wala Wala College or Harvard. The source don’t matter your parent, Scholarships, etc. Any schools and even top wealthy schools will evaluate your qualification first. If you are a winner of national merit scholarship such as ROTC and other merit based scholarships, it is a sign and confirmation that you are highly competitive and diligent to apply to such programs. It shows your commitment and maturity. This also sets you apart from your parent sponsoring your education.
Bottom line, it adds to your character and quality. So yes having won a merit based scholarship such as ROTC is a positive reflection on your application to which ever schools you are applying to. It adds certainty that the student has all serious intent to pursue military service through their schools. Based on my recent interaction with admissions and accepted students currently enrolled in ROTC Program at some highly selective colleges, about 50% are admitted to their as ROTC Scholarship winner. This is a small sample size so don’t take this to the bank. But it is positive.
For all those merit based scholarship winners, great job!