Yes, but it might take two coats.
You can buy 'sealing' or 'isolator' paints that are designed to cover damp stains, tobacco, etc from places like B&Q. They're reasonably expensive and you have to paint over them, anyway - so I'd just paint it and, if it needs, paint it again.
If you wash it...
I just got it done last night and I didn't notice it until this morning after my shower. There is a very visible line along my hairline where the dye stained my skin. It looks silly. I don't go and get my hair done often since I have two kids and another on the way, I would rather just spend...