I seriously hope not, I think that would look terrible, especially on a suit supposedly generated by light. It's one thing for these more Earth-bound street level heroes embellishing their costumes with a little dab of eye make up. But this isn't a suit he's putting on in a changing room or with prep time at the vanity in his secret lair. This is something the ring generates and throws up around him in an instant, in any situation, while he's running, in mid flight dropping out of a plane, or while leaping off the tarmac into space! The eye make up can't just suddenly be there.
Besides I don't really see the eyeliner in that pic. anyway. It just looks like the shadow cast in his eyesockets from the shades.
Since the suit is for the most part going to be CG anyway, I think there's no reason they can't bring it to the mask, and extend it to a proper edge around the eyes, or even better throw some translucent white tinted lenses over the eye holes, so you get the feel of the comic, but also it allows a hint of the eye movement and expression through the translucent lenses.
Also since everything on him is made out of pure energy fueled by his own thoughts and will, it can change and reshape slightly with his expressions, something you couldn't do with a stiff real material mask but only in animation or CG.
The reason movies leave the eyesockets open, and then fill in the rest with make up, is so you can capture the expression of the eyes, the little squints, or wider awe or surprise, or scowls or inquisitiveness etc..
This is not a problem with a partially animated or CG mask, because it can move right with the edge of the eyes and capture all of that..