You're young, so you might make it; but realistically, to really make it, IT is a full time job. Business clients are where the steady money is at, and you need to be on call basically 24/7 or at least 9-5 every day.
YMMV, but it can't hurt to try.
They either go somewhere else or wait, you get to sound like a bigger outfit and one that's busy. Plus you didn't lie to them, even if you're watching telly that counts as "occupied".
So I would recommend installing a free program like logmein.com on all client PCs you will be servicing on an ongoing basis. This way you can provide quick response time, even when you are unable to be physically at a client's site.
Hope this helps.