Do I need to submit a notice of intent to homeschool (NOI) to the school district if I enroll with an umbrella school?

No, and you should not submit one.

Students enrolled in an umbrella school are not subject to homeschool law. They are considered private school students, so a notice of intent is not required. When you submit an NOI, you are obligated to follow the homeschool law, which includes providing test or evaluation results on odd years starting with 3rd grade. If you have already submitted an NOI and then enroll in an umbrella school, it is recommended that you notify the district that you have enrolled in a private school.