No, Dropbox does not intentionally throttle the connections from third party apps. Note though that your connection speed to Dropbox depends on a number of different factors, which can vary over time, such as the routing you get between your ISP/device/app and our servers. Sometimes resetting or retrying your connection gets you a different route and better speeds, but that is outside of our control. Some ISPs also throttle sustained connections so if you see an initial high connection speed followed by lower speeds, that could be the reason.
It will also depend on the implementation of the third party application. The official Dropbox desktop app is custom built to optimize the connection to the Dropbox servers so it may not a good comparison for third party applications. Dropbox does offer a Performance Guide that developers of third party applications can refer to for information on how to optimize upload operations though.