Will a new stock ($200.00) and possible new blue help or hurt the value.
Not enough information.
A new stock won't hurt the value if you keep the original. Just don't toss the old one in the fireplace. New blue often reduces the value of a
collectible gun, because a collector would rather know what condition the gun is really in, and original is always more collectible.
Fixing up a non-collectible gun that's near junk status will improve its value, though generally not enough to justify the cost of doing it for resale purposes. I.e. you have a $100 gun, and if you threw another $350 at it, you might have a $250 gun. Either way, in general, an old A5 is a gun of very limited utility by modern standards. Even a beat-up Mossberg 500 can be used for skeet, trap, goose and pheasant, if it has screw-in chokes.
Personally, I would leave it alone. He doesn't need a
restored gun to learn about shotguns. Furthermore, I don't know what your son thinks about the thing, but having been a son myself, I can hazard a guess that he won't think and feel everything his father believes he should. Save the money for the next gun he'll get. It's a field gun with a fixed choke and probably a plain barrel, and let's just say the A5 is an "acquired taste" on several levels. If someone gave it to me for free, I'd take it, but it probably wouldn't ever leave the closet until I wanted a few bucks and sold it.