My doctor knows a lot more about sickness than I do, but I don't have to take my kids to see him every day to know whether they're well or not. I am with my children every day. I see how they're doing, I know if they're struggling with an idea or a technique, I'm available to help them if they wish. A suit off the rack may fit you fairly well, or if your body is non-standard in some way, it may be hopeless. The same applies to learning.
Kids like to learn.
Given freedom, encouragement and access to information, they will learn as much as their minds will hold, as fast as they perceive a need to know. But they may not do it in the order you'd expect. To answer the question in a different way, homeschooled kids usually score well on standardized tests. It must be very time-consuming. I am acquainted with one single mother and one two-income family who homeschool.