Are Gem Squash Edible After the Green Rind Turns Yellow/Orange?
Generally, aging/ripening squash does not pose any food safety problems. You can eat all members of the family. You just have to make sure that they are only overripe and not rotten. Rotten squash will have areas which are much softer than the rest, and usually somewhat slimy. 

It is a different matter if you want to eat overripe squash. Both the taste and texture will change, becoming mealy, or soft, or spongy, and the taste can get bland. You can try cooking it the same way as young squash. If this doesn't work, you can also try some recipe which masks the taste and texture change, for example something involving a puree or a coulis, and adds spices.