Question: Are there any benefits to removing unused using statements in a VS project (such as can be done using Resharper), or will VS automatically take care of that when building/deploying?

Answer: 
There aren't any performance benefits, if that's what you mean. 

All references in an assembly are fully qualified; the compiler merely uses the references you provide in your code to fully qualify identifiers, so the only impact of unused references in your source code is a slight decrease in readability (why is this reference here?), and a trivial increase in compile time.

To put it another way, the generated IL is exactly the same whether you remove the unused references or not.
Removing unused code, is just extra baggage and hard to measure the efficiencies gained.

* Removing unused code, brings down the compilation time, I am working on a project which takes anywhere from 15 to 20 minutes, there is tons of unused code. Eliminating unused code decreased the compile time to ~7 minutes. This makes a diff when there are many developers on the team, this saves everyone time to quickly build and test.
* If you have automated your build and unit tests, you have now removed unit tests you do not need. again this is reduced time taken to run unit tests. Just increased efficiency in your Continuous Build management process. 

	+ Unused code results in bigger foot print of your binaries. Having a smaller code foot print will reduce the time taken to load/start up initially. Though the gains may be very meager and subjective.