No, you can get rid of the corrosion with a wire brush (corrosion brush). Pull apart the hinge (if you don't want to do that, then you won't fully get rid of the corrosion, and it will always come back!) You could just remove what you see by keeping the door attached, but if you wanted to remove the corrosion fully, remove the hinge. Then, take a wire brush to the dissambeled hinge. Scrub the **** out of it, remove the paint, and remove the corrosion. If it turned to pitting corrosion, then use a drill and a sanding disc to fully remove it. (smooth it out by using a higher grit and smooth it out) Then once complete, use a corrosion prevention compound (you can buy these at hardware stores, or checkers etc) and spray a few coats on the untreated hinge. Wait for it to dry, then paint the exterior. Spray a few coats of gloss black, then grease the hinge (I recommend Marina grease (it displaces water alot better)) Then reinstall the door and you're done.
Chances of a sagging door (if you choose to disassemble the hinge) are pretty high. So it's either keep doing corrosion work on your hinge, or chance a sagging door.