I've never used a cotton ball for the purpose of starting a fire, with or without PJ. I do have PJ in my BOB, mostly in the form of something to protect my lips or an antiseptic ointment.

I have used a lip treatment PJ smeared onto a gauze pad to start a fire, just to see how it worked. It did burn with a couple inches of orange flame, until I could no longer tell what was burning. Seeing as it worked with a gauze pad, as much as it might with a cotton ball, I'd add more gauze instead of the cotton balls.