No. If you want to rescue them for soup, peel them, boil the shells in water with half an onion, a stalk of celery if you have it, to make a quick broth, throw out the shells and veg and keep the liquid.

Then put some butter in the pan, melt it, whisk in some flour. Once it's combined and a thick paste, slowly add back in the broth, whisking to keep it smooth . Then put in your overcooked shrimp till warmed, take it off the heat and add some cream and season with salt and pepper. Simple shrimp soup.

But no, it's not as simple as pureeing shrimp in the blender. That won't give you anything edible.

I mean, at least get the skins off first. This sounds horrible any way you do it.

Bisque is the technique you are looking for. But keep in mind that has you remove the shell pulp after cooking.

You'd be better off making stock from the shrimp, rather than trying to puree them and eat them. If they really are as far gone as you're saying, you'll just make a soup that tastes terrible.

On the other hand, if you make stock by simmering them for a few hours in a pot full of water, you'll be able to use the stock to make other dishes.

Look up bihon. It's made from ground up shrimp heads

you can make a seafood stock out of them, but, uh, pureeing the whole thing seems... a bad idea.

I don't know that you can recover already-overcooked shrimp, more than just by making the stock from it. (stock is the last step of recovering soemthing useful.) you could then use it for fish-based ramen, or other seafood stews and soups, whatevers.

I wonder what would happen if you used fish stock for things like rice (I use veggie or chicken stock for that all the time. It deepens the flavor of the rice.) In any case; if you're absolutely insistent on eating the over cooked shrimp, you could shell/skin them, and use that for stock then serve to the in-laws you don't like. save the good food for people you actually want to come back.

Don’t breathe this

Just learn how to quickly shell shrimp. It's not even hard.

Sure, go ahead. I have no idea if it’s healthy or edible though.