My immediate concern would be the ever-present voids you find in cork. The pen tip follows the surface, moving up and down with variations in surface relief (heights). If the pen passes over a void, the tip will drop into the void. But when it tries to move past the void it will get stuck… It needs to have a nice gentle ramp it follows up to exit the void. That is, the tip follows the surface but expects changes in height to be nice and smooth and graceful. A sudden drop isn’t necessarily a problem. But then exiting from that sudden drop is.
Soooo, you’d want to fill any voids beforehand. There’s plenty of wood filling compounds meant to do exactly that; meant to fill tiny voids caused by the grain in woods. These won’t be tiny voids though. However, there may be a second, beneficial effect of using a grain filler: it may seal the surface sufficiently that you get tighter lines (better sizing in typography speak). With coarse, absorbent surfaces the ink soaks in a spreads out making the lines a bit fuzzy. With a slight seal, that effect will be lessened and the lines will be crisper and thinner, better matching the pen tip’s width. (Chicken eggs vs. duck eggs can exhibit this: the more porous chicken eggs have inferior sizing compared to duck eggs.)