Sanding will get rid of it.
I am doing work for someone who has an apartment that had carpeting that was put on top of hardwood floors. I pulled the carpet up as well as all of the staples and such, but the floors have random paint droppings from whomever painted the walls last. I've had "success" both with using a razor blade and using Goof Off, but they both take a long time...the owner has a professional company coming out tomorrow to sand the floors then spread new polyurethane. If the sanding will take care of the paint then he'll just leave it for them, otherwise he wants me to continue scraping.
So will the sanding be all it needs to remove the paint?