I believe the only way to use those EAX functions that are included in Sound Blaster systems is to use that system as your Windows Default Playback Device. Windows can only use ONE device for output at a time. You get to specify which output device is used by Windows for three functions: Default Playback, Default Recording, and MIDI. This is done in Control Panel ... Sounds and Audio Devices ... Audio tab. However, once you choose the on-board audio system, the output will NOT be in the HDMI cable, and normally there is no way to route it through there.
So, your choice then requires that you arrange a separate cable from the rear output panel of your mobo (from its stereo Front Speaker audio jack) to an audio input of your monitor...