Yes! Search for "mushroom ketchup", and you'll find various examples for sale. Whatever kinds I've had are nice on bread, and really nice with eggs, but I wouldn't want to eat with chips / fries.
You can still sometimes find mushroom ketchup in UK supermarkets. It tastes a bit like Worcester sauce (spicy and 'brown' tasting), but milder as it has no anchovies in it.
