I imagine it would be tricky to get the whites firm enough and yet keep the yolks runny enough. Is the *pickled egg* the main point of the exercise? Why don't you separate the raw eggs (save the yolk), and poach the whites till cooked through, and then pickle them? If you put the whites in a small custard cup or something similar, put a top on it (I use wax paper and then aluminum foil when I do this with whole eggs), place the cup in a pot with simmering water coming halfway up the side of the cup, put the lid on the pot, and simmer till set - 15 to 20 minutes. The final pickles won't be egg shaped, but that shouldn't matter much.
