In a perfect world… it would work like that, but it usually doesn’t for a number of reasons.
1. Most of these sites make you go by an alias nor do they maintain your ‘entry’ into the contest. You can’t link back to your own portfolio, because that encourages off-site communication, which enables you to get around the commission the sites charge the contest owner.
2. Even if I designed the site - I don’t want Johnson & Johnson feminine hygiene products linking back to me. Any legitimate company that will develop a long-term relationship with you, which is a designer’s bread and butter, will never agree to a link-back. Besides, it’s not hard to get incoming links these days, from relevant/related sources that Google will actually award you for, just do something worthwhile.
3. Rarely, rarely happens. I have actually seen a lot of these sites claim that the designers lose their rights to all of the entries, not just the winning entry. Besides, why not just submit the designs to graphicleftovers.com in the first place - eliminate the period of “I wonder if I’m gonna get paid for that 6 hours of work or not.”
4. The chump change made from these contests reveals very little about the possibility of being self employed. Sure, you can have other people tell you your work sucks and you’ll never eat again if you go solo, but you probably knew that before you started. On the other hand, by going and getting a job with a design firm (even a small one) you would make more money per hour, be guaranteed to be paid for the hours you worked, learn how the design business is much more than graphics - it’s about analyzing the company and it’s audience and being a psychologist with a paintbrush, and receive valuable insight into the business behind the design business.
Not trying to knock these sites really - I’m not a designer, I’m a programmer/entreprenuer who uses the hell out of these sites? Why - because I’m a bad person.
These sites give me all the power within the relationship, allow me to see the maximum number of design concepts for as little money as possible, and give me a final product for as little money as possible. Worst case scenario - I walk away with something I don’t want but I can release for free on my blog and instantly get a couple hundred inbound links (templates, converted to Wordpress templates are a couple hundred thousand).