I think it's a poor idea.
A set of backup snapshots is not the same as source control. Your source control history is a story you tell about your code. Each commit is an important event, encapsulated on its own, with a person to blame and a text description and a definite date. Whereas a history of file changes is just a history of file changes.
The other point to make is that there is only one timeline of file changes. That is far too one-dimensional for code development. You need the ability to branch.
Using Dropbox for source control is like publishing an hour-by-hour activity log and claiming it's your autobiography:
9 am: Typing. Still breathing.
10am: Typing. Still breathing.
11am: walking to lunch, breathing faster
noon: eating.
1pm: typing. Still breathing.
You want a system that tracks the deliberately edited, important points of the story. You
also want backups, of course, but they don't accomplish the same thing.