Dropbox has an abuse detection system in place to detect and prevent automated logins to help protect our users. It uses a variety of factors to decide whether or not to display a CAPTCHA or verification challenge like this, so whether or not you see it, or exactly what you see, may vary over time.
Dropbox doesn't provide a way to bypass these for testing, but I'll pass this along as a feature request. I can't promise if or when that might be implemented though.
