I have used brush on bed liner for some corks. The paint had no adhesion issues. However, it did not fully protect the cork. It was easily broken in soft spots in the cork.
My guess is that bed liner is very tough due to being bonded to hard metal. Without the metal it seemed too flexible to hold up. I didn't have catastrophic failure, but failures none the less. Water seeping into the cork can't be good for longevity. I went to epoxy as a result.