Yes it does look to support 7.1 surround. However those headphones are stereo so you wouldn't use 7.1 with that headset.
That headset is 19ohms so the motherboards amp should be more than enough to power them. I use the onboard sound of my ASUS Z270F with a pair of harder to drive 50ohm sennhesier HD558s and it works fine. You could likely get slightly better sound quality with an external DAC/AMP but you don't need one.