Brown,
It will flash your eMMC but this would require some effort.
Basically, the UniFlash support AM335x devices through loading a boot loader and a uboot onto the device, and then talk to the uboot through a debrick script, which basically instruct the device to grab a set of files from the host tftp to update itself. Therefore, as long as the uboot you are using can support eMMC flashing, it should be possible.
It is important to note that the board/setup you have also need to be able to boot from USB peripheral for this to be possible. And you should only use the Windows ver for production. The Linux version is for engineers to verify their package. It is relatively unstable due to the unreliable dependencies from ubuntu.
I advice you to try to do this manually first to test and debug on your setup, then write the debrick script that describes how to load your files to eMMC.
The debrick script have some degree of flexibility. You can ask the expert in the Sitara forum regarding the detail. Schulyer Patton is the author of the script format. He could help you with packaging the files when you are at that step.
Regards,
Victor