I did AmeriCorps for two years with a literacy nonprofit and it was one of the most challenging yet rewarding experiences of my life. My GPA and GRE were fairly average, but I believe this experience helped me stand out and get accepted to several programs. AmeriCorps is tough--you're not making much money, and the job is demanding (psychologically, emotionally, and physically). But joining AmeriCorps and successfully completing a term or two or service shows determination, strong work ethic, a desire to give back, and perseverance. Also, you'll get hands-on experience working in a strongly related field which will give you lots to draw on for your personal statement. On my resume/CV, I listed it as "service" experience because like you, I wasn't sure whether to list it as work or volunteer experience since it didn't seem to fully fit either category. From the schools I talked to, service experience like this is highly valued. I think it may help give you an edge over other applicants.
Also, you're eligible for an education award after a full term of service that you can apply to existing school loans or a future program. When I did it, I received $5,500 per term, and my total award after two terms paid for my entire first semester of grad school (housing, books, tuition, food, etc).
Hope this helps!