Is Demonstrated Interest Important at Public Flagships?

Depends on the school. Check the school’s common data set, section C7, or its admissions entry on http://www.collegedata.com .

For example:

Michigan considers level of applicant’s interest: https://www.collegedata.com/cs/data/college/college_pg02_tmpl.jhtml?schoolId=379
North Carolina does not: https://www.collegedata.com/cs/data/college/college_pg02_tmpl.jhtml?schoolId=1600