I haven't actually tried to use that type of pump sprayer for the use you are suggesting, but I would think that it wouldn't work well with the thicker type of fluids involved. These type of sprayers are designed for water based liquids, that flow easily.
The idea is intriguing. I bet it wouldn't be hard to drill out the nozzle to a larger diameter, but I still think the oil would be too viscous for that to work well.
I saw a $10 drill pump at the hardware store the other day, I'm wondering how well that would work. I hate laying underneath the truck with the hand pump.