Simple answer is no.
Extended answer is mysql can log queries, however it has limits, and if there is even one difference between the environments it would lead to those queries not functioning. Even with that the only way to do it is though the server itself, since as far as I am aware there is no special logging added to JDatabase (Also if a component does not use JDatabase then the control lowers even more).
With the above you can see in a perfect world, there is a way, however if you move from dev to live, you currently had a live site that was doing queries on its own and it is "different" then the current dev/staging version. So if a user signed up on the live site, and you upgraded Joomla in dev, then the update to the users table would add the need to manually re add that user (there could also be changes to the table structure). Now imagine its not one user, but 10, or even 100, and the process cannot be automated.
Joomla has some nice updating features, allowing a version for version mysql update on the tables, this ensures the tables keep the structure the queries need, however it does not track any inserts or updates on the tables, so if you update in a dev environment, the best way to update in production is to just follow the same steps and update in your production as well.
In the future it may be possible for Joomla to track database changes in its core, allowing you to sync a production version to a development version, however the amount of work to build something like that is crazy, and would have an impact on performance. Right now I do not believe there is, or should be any plans for it.