Am I able to control the rendering intent for jobs that contain embedded CMYK and RGB profiles? How about the included intent? Is it used?

Yes for both CMYK and RGB. The embedded profile workflow actually follows the CIE path which in the expert color settings UI is the same as the RGB path (however it might not be labeled). Thus the rendering intent (or style) selected here is honored for your embedded workflow. Additionally, since this selected intent is used, the embedded intent is ignored which is typical in PostScript workflows.
NOTE: Please understand that the option "Use PDF/X Output Intent" will use the intent contained within a PDF following the PDF/X standard and maintain those intents defined in the PS stream. This can lead to undesired color results if the workflow is not understood. Namely, the default intent is typically relative, where that for RGB on the Fiery is Presentation.