Done the old grill and headlight bezels on my '91. I was able to peel the old chrome off of the bezels, only scuffed the chrome on the grill.
After a year's worth of driving it the bezels still looked good. Grill lost paint at bug and rock chips and showed the chrome underneath.
If you are going to want it to last, regardless of what you apply paint or bed liner, you need to get the chrome off. If there is any chrome, the paint or liner won't stick long term.