My first impression is that of course this will not work. But let's be more positive. What would work?
1) Use your SVN server to maintain versions and history and then checkout a working directory to the dropbox. You can even have multiple working directories in the dropbox. 2. put your SVN server in the Internet. Run it on any computer you might have. Old notebooks make good low volume servers. All you need is a home DSL line and dynamic IP.