The fraternity will be suspended for at least four years.
The president will participate in this week's Board of Trustees meeting remotely.
Parnham will travel out west to the Denver Outlaws.
The captain was selected by the New York Atlas.
Despite scoring only two goals in the first half, Penn State tied the game in the third before falling just short of the final.
"My Penn State experience helped transform me, and I just want to do what I can to help students. And when I say that, that's the umbrella, and then everything else falls underneath it."