Will paint adhere to bed liner?

While installing my LEDs under the bed railso recently I thought it would be a nice touch to paint the "TUNDRA" stamped in the front of the box. I have the factory sprayed bedliner and wondering if and what type of paint would adhere to the bedliner?
Thanks in advance!

 

My initial thought is no. That being said I have never tried to paint bed liner. I would try a DIY colored bed liner that you can brush or spray on. Something like this
http://www.monstaliner.com/forms/monstaliner_colors.htm

or

https://duplicolor.com/product/bed-armor-truck-bed-coating-aerosol

Looks like that monstaliner comes in a much wider variety of colors