No, the result would be far too hot. Actually ketchup would work better although you would want to taste the result and modify it depending on theingredients at hand. At this point a bit of sarancho...
For red spaghetti sauce, tomato sauce is often a primary ingredient. Tomato paste is added to thicken the sauce, and spices such as oregano, garlic, basil and onion give it the distinctive "Italian"...
Cocktail sauce is a red sauce that is tomato based and slightly spicy. A mayonnaise sauce as the name implies has a mayonnaise base which typically has lemon juice and pickles added.