I probably should write a long rambling post about being in Philadelphia, homeschooled, and doing FIRST.
I should say first, that the Philadelphia School District requires schools to allow homeschooled students to participate in extracurricular activities at schools. That being said, being on good terms with the team/teachers is a plus. As a homeschooled kid, I tended to spend massive amounts of time at the library, and the teacher of Science in the Summer, a summer science program sponsored by (at the time) GlaxoSmithKline. The teacher (yay Ms Liberman!) happened to be the lead teacher of the robotics team at GWHS (304), and invited my brother and I to the team. After a bout with the School District lawyers, we both joined the team, and it went from there.
I'm not sure how friendly the current school district of Philadelphia teams are to homeschoolers, but (and I'm sure this applies to a lot of schools, teams, and districts) if you get to know the team and the mentors, you have a team to join. It's not hard: come to an event and talk to teams.
/end of rant. Just my $0.02