Yes, you can.
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.
Many children enroll in PRS and attend publicly funded enrichment programs with no issues. Keep in mind that many public schools and districts may not understand what an umbrella school is. Please contact PRS if you need assistance.