I'm running VS 2012 and Visual Fortran Composer XE for Windows with IMSL (2013) currently, but will need to move to VS 2017. When I do, will I need to purchase an updated Visual Fortran Composer, or will what I have work with VS 2017?
If you wish to continue using Visual Studio for non-Fortran development, you will need a newer Intel Parallel Studio XE (the current name of the product) to work with VS2017. See this article for compatibility details.
You will probably have to update to a newer IMSL as well.
If all you are doing is Fortran development, you can use the included Fortran-only VS support based on VS2015. An alternative is the VS2017 Community Edition, which is free, but check the licensing terms to make sure you qualify.