As with anything else, YMMV.
The known facts are that as far as federal financial aid benefits (Pell Grants, Federal Loans, federal work study) are concerned, your ROTC scholarship has NO affect. You don't even report it on FAFSA (Use the search function to find the threads and links that clarify).
As far as institutional need-based grants, most schools will require you to report your ROTC scholarship. They may or may not adjust your need-based aid accordingly. This is entirely within their powers.
As far as merit-based awards, you may want to investigate as to whether the award can be used for either tuition or housing charges. Many schools do not allow their awards to be used for charges other than tuition. In these cases (particularly at lower cost public schools), you may want to look at using the ROTC scholarship for housing and do the math as to which is better for your wallet. What the scholarship is paid for can be changed from term to term upon filling out the appropriate form.
In all cases, your school's financial aid office is the best source of how things work!