Does OMGF (Pro) support FontAwesome?

No.

OMGF stands for Optimize My Google Fonts, and — as the name suggests — only deals with Google Fonts. 🙂 With a small exception for the 
Apply Font-Display Option Globally option, which applies the font-display (swap) attribute to every @font-face statement it finds.

To automatically host FontAwesome (and other — non-Google — icon sets) locally, try out my other plugin;
GDPRess.