Proceed with caution. I have never (in 25 years of car care) seen a touch up product for that cheap that actually works. Even the more expensive T/U paints can still smear and dribble easily.
I empathize with your situation. My beautiful Neuspeed RSE10s that I waited 4 years for have some nasty rock chips from normal highway driving. It kills my soul each time I air up the tires or wash the car and see the damage.