I rather doubt that. Nobody does really good work at that rate, not in this field. Cheap programmers do legendarily shoddy work on projects of any scale, and the employers worth working for know that.
Offer great work at a fair wage, and you'll be fine.
To paraphrase Howard Taylor, if you want to succeed as a freelancer, you need to be (A) the very best at what you do, (B) a great communicator, and (C) everyone's favorite person to work with. And I'd add that you need to be able to prove to a prospective employer that you are those things.
My strategy starting out has been to communicate relentlessly and deliver spectacularly. Really understand a client's needs and ask a lot of questions (and make a lot of comments) about a project before even putting in a bid. Do tiny $50 trial contracts well and quickly, and then offer to finish the job at a fair price. Always respond to messages the same day. Always get working software into the customer's hands as fast as possible, and polish the living daylights out of it jointly.
If you're awesome and people know it, nobody will want to hire the $10/hr crowd when they could get you.