It'll more likely than not have a coat of sanding sealer (like clear primer) on the wood before the black was applied, so the black shouldn't have gone into the grain at all.
IME the face of a headstock is easy/quick to do because of the small size, you don't get bored of all the contours and edges like a body, so don't end up rushing it, then subsequently wishing you'd spent more time doing it properly.
Top tip when lacquering a headstock face. Mask everything you need to but leave about 5mm down the sides until last. Once everything but this area is masked, run a length of masking tape around the perimeter of the headstock but about half a mil down the side of the headstock, rather than try and get it exactly on the 90ยฐ of the face/side. It is infinitely easier to get a nice line this way. Once lacquered but still wet, CAREFULLY peel that last strip of tape off that you put on, the wet lacquer edge will flow out and not leave you with a sharp masking edge, as it would if you let it dry first.