You've got a wp.com-specific question, so that's great that it's here. But if you have any competition-specific questions in the future, please head over to the Sandbox Forums. Cheers.
Anyhow, Andy will be rolling out an update to the Sandbox to all wp.com users very soon. Don't worry, both the 0.6.1 and 0.9.x versions of the Sandbox will exist simultaneously and separately so that not a single persons style sheet is broken until they've had the chance to update.
There are quite a number of CSS class changes/improvements to the core of the Sandbox, so you I strongly advise against starting with 0.6.1. I just don't want to create any extra work for you.
Now, anyone can compete in this competition, regardless of whether or not they have a blog on wp.com, a hosted WordPress install, etc.
Because you really, really want to do your designing on a local install of WordPress. It's faster and you will be much, much more productive.
Basically this means installed a mini-server on your computer (Mac or PC) and then running WordPress there. You can do all your designing locally. I strongly encourage you to do this as well.
There are lots of tutorials on how to install WordPress locally, a sample of which you can grab at
So yes, the competition and available to absolutely anyone. The real benefit to wp.com users and what makes this comp different than all the previous theme and plugin competitions, is that after the competition finishes, all the designs will be CSS and images only, so anyone with the Custom CSS upgrade will be able to use them.
Let me know if that helps. ;-)