I faced this question recently due to a security review of an ArcGIS Server site I'm involved in building. You are correct that ArcGIS Server uses Apache - Apache Geronimo (which itself is built on Apache Tomcat, in case Geronimo isn't one of the choices available for signing your CR). I ended up generating two certificate requests - one for IIS, and one for ArcGIS Server.
In case it's of interest our authentication tier is GIS Server, and we have the Web Adaptor and ArcGIS Server installed on the same machine.