To serve php files, the webserver has to create the content. Dropbox does not allow this to happen. When you are seeing pages in Dropbox, the browser is rendering them. It is the same as having an .html file on your desktop that you open in Chrome or something.
If you want to server php files, you need a webserver that has php installed.
You can install Dropbox on your server (VPS or with certain shared hosting providers). From there, you can place your site files in your desktop’s Dropbox and work on it there. Any changes you make it will automatically sync to your server. It’s also a great way for automatic backups.
I have no clue if this is a good thing to do – however: I moved my whole dropbox folder to xampp/htdocs/Dropbox
And it’s just fine – I can execute phpfiles wherever I wan’t in my project folders.
So no problem.