It can fit, but it depends on what you end up doing. I really struggle sometimes when two client deadlines converge (even though they weren't meant to...delays on their part, or emergencies) and then I have to squeeze more work into a day than I have room for.
Did you have any specific questions in mind?
A friend of mine combined maths tutoring with being a CAB volunteer - she definitely finds the latter v fulfilling.
If you're new to being self-employed I recommend you hop on to the MN discussion board about that.