I would be interested in removing the recoil pad, not to see how far the crack goes, but to perhaps see what caused it. Many guns have had large holes bored into the butt to either remove wood to reduce weight, or to add weight to change the balance of the gun. Your crack may simply be a stress crack caused by the maker using a piece of walnut that wasn't fully seasoned. Or it could have been cracked in a fall or by dropping the gun.
But I once purchased a Lefever G Grade that had a similar crack, and the buttplate was also slightly warped outward. I bought it, suspecting that someone had packed lead into a hole in the butt. And when I removed the buttplate, I was not surprised to find that a rather large hole had been packed with lead shot that had swelled and oxidized heavily, causing the stock to develop a longitudinal split. It was a fairly easy repair after digging out the oxidized shot, blowing the dust and debris out of the crack, repairing with Titebond II wood glue, and clamping with surgical rubber tubing. I then turned a walnut dowel to closely fit the large hole, and epoxied that in place for further reinforcement.
Your recoil pad is already misshapen and deteriorating so I would not be overly concerned about damaging it. Down at the bottom of those two small holes you describe are the screws securing it to the stock. All of the few pads I have removed have used Phillips Head wood screws. You should use a well fitting round shank screwdriver, and lubricate the shank with liquid soap so you don't tear or damage those holes any worse than they are. Actually, those holes should be near invisible slits cut with a razor knife, and again, the screwdriver shank is lubricated so that after the pad is installed and cleaned, the slits would not be visible. I'd bet the cost of a good professional crack repair and refinish will exceed the hit you will take in value selling it as is. So you may just want to leave it alone, and let the buyer worry about it.
This gun has automatic ejectors, doesn't it? And it sure looks like the frame, lock plates, and top lever have been coated with something like black lacquer, which is flaking off in places. The crack behind the lock plate is a fairly common malady found on many L.C. Smith guns. If you ever saw how fragile and thin much of the inletting is behind the frame, you'd wonder how they all don't split like firewood.