I started using freelancer.com. It's honestly a pretty bad site, unprofessional in a lot of ways, high fees, etc. I got low paying jobs that took a decent amount of work, although the quality of work expected wasn't too high. However, it allowed me to get some light experience to start which was useful, and as I finished projects and got all 5-star reviews (my point is not that I was super wonderful, but that if you do decent work and communicate well, clients will like you) I began to get more involved, higher paying jobs. It got to the point that I no longer had to actually use freelancer.com to find work - people I had worked for in the past or other connections I had made while working would contact me asking for things. This was great for a couple of reasons - no website fees, good long-term relations with trustworthy clients, no time spent hunting for jobs, etc.
In short, if you're willing to put up with the bad parts of freelancing websites, you can probably use it as a step towards much better work.
Same. Started on Elance and underbid to play the game and just get some gigs. Over-delivered on projects and got all 5's on reviews. Built a solid reputation and profile to the point where I get about 5 invites a week, most of which I turn down. Raised my rates three times in less than a year (have more than doubled) and am able to pick and choose what work I take on. It does suck at first, but carving out a niche can really help if your niche is an advanced method/tech/service. The high paying jobs are harder to find, but they do exist and are waiting for people who know their stuff. My largest client to date was found on Elance and I never would have known who it was from their posting.
I think it's definitely possible. I think more important than where you are from is your grasp of the (spoken) language your project is in and you are communicating with. So if you're communicating with clients in English, writing your code, documentation, and visible interface in English, it's obviously important that you have a very good understanding of English. And as long as you do, I don't think being foreign would be much of a hindrance.
In short, if you're willing to put up with the bad parts of freelancing websites, you can probably use it as a step towards much better work.