I doubt I would be perceived as sulky because people would be used to the withdrawal, and they wouldn't dream I was doing it because of emotion, as I appear very unemotional.
How I deal with things depends on the cause.
--When I am stressed on schoolwork or things out of my control, I tend to revert to my tert & inf functions (Ni/Te) and go into total INTJ mode - getting things done, cleaning, organizing and planning. It's rather convenient, actually.
--If I'm trying to work through emotions I don't understand, I generally analyze in my regular mindset and try to work out why I feel them and whether it's reasonable to do so or will do any good.
--I've had very few interpersonal relationship issues because of commitment issues. I can definitely picture myself "debating with myself" (convincing, then switching sides) belligerently in relationship issues - "Well, this is your fault, you should have done this, this and this, while I should have done this because...- really? you agree? But this part wouldn't work because this! ha!" and once I've done that, go bazonkers and try to prove a stupid point with big words just to see if they catch on. Fighting, INTP fashion

I cannot, however, picture myself withdrawing/sulking and staying emotional, because the reason I withdraw is to think things over, and I can't see myself staying emotional if I did that.
-- I had issues with existential depression in the past. I would occasionally get into a cycle where I didn't understand why I was upset (because I can't understand why!), which would upset me. Slowed thoughts, dropped grades/times, etc, but although I appeared more snappish/uncooperative/reclusive, I don't think I sulked.