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.