Believe it or not I've actually done exactly that.
It is not going to get "into the engine". It'll just get stuck in the cylinder head, usually right behind the water outlet that is bolted to the cylinder head. Will it cause problems? It can reduce cooling system performance, and with the engine spun around backwards in the frame, it needs all the help it can get-thus I recommend every attempt to remove the bolt. If push comes to shove, pull the engine and then remove the water outlet, remove the bolt, reinstall with new gasket (after thorougly and completely removing the old gasket), and reassemble. New coolant of course. Removing the engine isn't really that hard on those, I have haphazardly don it in about an hour & a half, closer to 1:10 if I hurry. That's just removal. Reinstallation is almost always slightly longer. Leave the fan on the engine, it will come off, but you will have to kind of bend the fan blades to get them OUT of the shroud. That's the worst part.
I had one of those old mowers, and gosh I miss it. Great mower!!
I bet that you can fish it out with a magnet. It shouldn't have gone very far.