Hi Leah Creiglow,
The GeoEvent SDK comes bundled with GeoEvent Server as part of the installation files. You can find the documentation and samples for it at the following locations
Windows: <ArcGIS Server installation directory>\GeoEvent\sdk (for example, C:\Program Files\ArcGIS\Server\GeoEvent\sdk).
Linux: <ArcGIS Server installation directory>/GeoEvent/sdk (for example, ~/arcgis/server/GeoEvent/sdk).
If you have seen it already, the documentation only shows examples using the Eclipse (Java EE edition) IDE.
However, in theory, as long as you have the proper components installed on the machine per the documentation (i.e. Java SE Development Kit, Maven, etc) then you should be free to use Visual Studio for your development needs. Since each IDE will differ in terms of what it will need to write, format, and compile the code (plug-ins, packages, and the like), we cannot really give definitive responses as to which to use, because there can be several routes you can take to accomplish what you need to to build custom connectors, transports, processors, etc.
I hope this helps somewhat or can give you an idea of how to move forward. Perhaps fellow end-users who have tried Visual Studio in their development can give more specific examples.
