Depending on the BIOS, you may be able to set up displays across both the integrated and discrete cards. For instance, mine can do it, but it has to have a specific option enabled in the BIOS/UEFI.
That specific Motherboard you linked does indeed support Flexible Display Interface, which is what is supposed to make even an i3 work with 3 monitors (though they all have to be the same resolution / refresh rate), and is also apparently required to allow the onboard graphics to work with a discrete card.
I would order a system with the motherboard, see if I can't get the i3 to work at an acceptable level alone, and if not, then spend the extra $60 or so on the discrete GPU.
Note that you will need a monitor that supports both VGA and DVI, possibly to include HDMI, but you can convert that to DVI via cable. Otherwise, you'll need the card anyway.