Yes, but it’s best to check with the district ahead of time.
The law limits enrollment to only one publicly funded program at a time. Since umbrella schools are not publicly funded, this isn’t a problem. The district may ask you to submit a notice of intent (NOI) because they will assume you are schooling under the homeschool law. You may submit your PRS Statement of Enrollment instead.
My own children and others enrolled in PRS attend publicly funded enrichment programs with no issues. However, it is important to know that individual school districts may have different policies and may not understand what an umbrella school is. The best approach is to ask the district and work out any issues before enrolling. Please contact PRS if you need assistance.