Home schooled kids here can and do participate in extracurricular activities. I don't think the local school can deny them even if they wanted to.
Home schooling was very rare when our kids were school aged, at least where we were living. I have mixed feelings about home schooling. Here, there is no academic qualification for the parent to meet, but students are required to take an annual academic achievement test or review by a certified teacher.
Maine DOE - Requirements, Forms & Laws
According to the above link, "During the 2011-12 academic year, 4,730 Maine students were registered with their local superintendent of schools and the Maine DOE for homeschooling."
"Maine's public schools educated 186,906 students as of April 1, 2011. The schools they attend employ 16,450 teachers and 35,487 other staff members.
During the 2010-11 school year, 13,489 students attended private schools, and 4,777 students were home-schooled.
Maine's public-school students attend school in 164 school administrative units run by 120 superintendents. Those units operated 604 public schools during the 2010-11 school year.
For 2009-10, Maine high schools recorded a graduation rate of 82.82 percent and a dropout rate of 3.46 percent."
The previous governor did a shoot from the hip at school district consolidation to save on admin costs, but it hasn't been a universal success and has met with plenty of resistance, especially in rural areas.