If Underdog wants to do if for the experience, I agree, go ahead a put it together. However, I wouldn't put a dime into it. Doing a fingernail drag around the scored cylinder doesn't let you know if it's out of round. From the wear pattern on the cylinder and piston, you can pretty much bet that it is. I'm certain that the engine will run but it will burn oil, be noisy (for a Honda), and will also be low on power. I'd put it back together nonetheless just to see how long it would last in that condition. I repeat that I just wouldn't put money into it.
When I buy Honda products, I make sure I get the "GX" engine. It's a bit more expensive but it will outlast a GC many times over if properly maintained. These B&S snow engines are not much different than the Honda GC series engines. No iron cylinder sleeve. I wasn't too concerned with that aspect because the B&S engine I have is on a snow thrower. Cool operating temps and clean environment will help to extend it's life. If it does blow, I'd certainly make sure I replace it with an IC series or better yet, a suitable B&S Vanguard which is made in Japan.
So, go ahead. Put it together and keep let us know how it runs.
Being an over head cam engine, you'll have to make sure you have the timing gears properly aligned. There should be indicators on both gears and the manual should also tell you what position they should be in.
