heres a thread to read about alc1150 vs a cheap soundcard like the dgx
http/www.head-fi.org/t/685163/a-researched-question-about-realtek-1150-vs-sound-card
will your motherboard support the ag1x? sure, i would not see why not. with that said, its certainly not the same as having a decent soundcard but whether or not you care enough to use a soundcard is another matter entirely.
generally using onboard is suggested unless you experience problems or are in a situation where a soundcard is required. things such as having distortion, static, etc or cases where your onboard is not powerful enough for a certain headphone choice.
the ath-ag1x is based on the ad500x / ad700x level of headphones so will have a wide soundstage, good positional accuracy, crisp response but will lack any deep bass response. they will have somewhat punchy mid bass but without much depth/power. this is the design of the headphones and is why they make good gaming cans.
if buying the adg1 is more expensive than getting a ad500x or ad700x and modmic consider the latter. amazon shows them at $300 right now which is far too much to spend given a ad700x is $98 and a modmic is $55 and there is no real difference between those two options.
tldr: test with your onboard first, you can always upgrade to a soundcard later.