I have done many wood projects with boiled linseed oil, the foot stool that I am currently using is one of them, and it absolutely does dry. It is always ready to re-coat after over-night. But, it has to be wiped on, allowed to sit for a minute or two, then, very important, wiped off. Also be super careful with the soiled rags. Mine go directly into the fire, or get spread out in the open to dry. Tossing them wet into the trash can could potentially cause a fire.
However, using it to finish a drawer will have no affect on whether the tools inside them will rust or not. IMO. Before I had heat in my detached shop, I would liberally spray everything with WD 40 in the fall, and that seemed to help a lot.