I received this question from a reader in Flagstaff. Let me share what I found out.
1. It depends on the district. However, most counties do allow it, you just usually have to work it out directly with the school and/or district. Make sure you arm yourself with information. At the time of this blog post, this website had the best links to the county eductional websites with the information you need.
2. Yavapai County Education Service Agency says this on their website:
Participation in School Activities
School districts are required to allow home schooled students to participate in interscholastic activities. The home schooled student must meet the same eligibility requirements, such as passing grades (as certified by the parent), as regular students. If there is a charge (Pay for Play, etc.), the home schooled student must pay the same fee as other students. Academic activities are not the same as interscholastic activities. Schools can take a home schooled student for any number of classes if the district wants to. However, unless a student is enrolled for at least ¼ time (as applicable to age of student) the district receives no state aid and is under no obligation to take a home schooled student.
2. Coconino County Education Service Agency also addresses this topic. Just access their document by clicking on Public School at Home link and find the section about Interscholastic Activities.
*The information on this blog post is based on a quick internet search and has not been tested or proven. Please comment on your experience with involving your homeschooled children in public school classes and/or activities.