I find it interesting that summer camps can count... my oldest is a boy scout an will be going to summer camp to earn merit badges in Environmental Science, Reptile and Amphibian Study, First Aid, Archery and Archaeology. So those days could be counted as homeschool days? I guess I could use the merit badge books to provide documentation, huh?
Yes, it counts. It's important to get out of the mindset that learning only happens when it's planned, scheduled, directed, or approved by someone else. Children learn the most, and retain what they've learned much longer, if they're the ones who initiate it, take ownership of it, and/or have input into what they're learning. I don't know of any research that doesn't support this fact.
Traditional schools don't allow student-led learning because teachers don't have time to mentor/facilitate a class full of students if each of them are learning different things, and it would be too expensive for them to provide the resources for each individual student even if they did. (And because all the materials would first have to be passed through committees to make sure they're "suitable" - however they define it.)
As homeschoolers, we don't have any of these constraints. So just remember that children (and adults!) learn 365 days a year. It'll be your job to document 180 of those days (if you're a SC homeschooler).