No. That pad isn't cork. It's micarta. A type of composite plastic.
Micarta - Wikipedia
I'd say to go ahead and strip the old line off and soak it in warm water for a couple of minutes. Clean off the old grime and crud with a soft toothbrush and some q-tips.
Don't lubricate this pad/drum surface or you'll be scratching your head why the drag no longer works. Simply clean the pad and the drum riding surface with a Q-tip and maybe some alcohol. Don't use alcohol or vinegar or any other solvent other than water on any of the painted surfaces of the frame or it
will come off. Don't ask how I know........
Lubricate the spindle with a drop of reel oil. I use Reel-X. Apply a small amount of grease to the drag adjusting screw and the drag plate top surface where the detents are (where it makes the clickety clickety sound). A very small amount applied with a toothpick will suffice. Quantum Hot Sauce is one of the best greases out there for reels.
That's about it.
Riptide's mention about screws getting lost on these reels is a fact I wasn't aware of. But makes sense. I'm afraid this reel has lost a screw or two in it's life.
These reels are so simple it's scary. Inexpensive, simple and tough.
The Pflueger Medalist was one of the best selling and most copied fly reels ever. There's a reason.