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.
Yes - I can think of two primary benefits:

1. Beyond its primary functional purpose (i.e. to reduce code verbosity), the 'Using' statement list at the top of a code file can tell future readers (especially those without Resharper) which namespaces are (or at least *were*) relevant to that code file. If you actively prune this list, it can act as a better signaling mechanism.
2. Removing unused namespaces will reduce the number of autocompletion candidates in your text editor as you type. If you rely on the autocompletion lists at all, this will help keep you "on the straight and narrow" and may even increase your typing speed, as you should be able to find your intended autocompletion candidate just a little bit faster.