Should patina be burned (wok seasoning)
As long as the surface isn't rough (i.e. with burned-on bits of food) then yes, the patina should be a dark brown or black.

That's more-or-less what a patina is; it's essentially tarnish, the result of cumulative oxidation, which normally happens to some metals anyway but is accelerated by the rapid oxidation of oils via high heat.

If you end up with a slick, evenly-distributed black layer, then you've seasoned it perfectly. If it's streaky or splotchy then you need to start over by scouring it down.

(P.S. Carbon steel is different from, for example, cast iron, because the latter is porous and you'll never see that perfect black, just a noticeable darkening.)