Personally I would poach them in water and then flip them into the tomato sauce when they were cooked. If you have really fresh eggs, particularly free range ones, and of those the blue/green ones are best, (though smaller) the white holds together so well, you might like it directly in your tomato sauce.
I make asparagus soup a lot for dinner when I don't feel like cooking much. I make poached eggs for protein, and I do cook them in water dab on paper towel and then plop in my thick soup. Sprinkle with a little Parmesean/Romano mixture and I have supper.
My asparagus soup is
1 bunch of aspargus, tough ends removed
about half a carton of chicken broth or equivalent homemade (which I usually have, just used the half box for a quantity)
1 small onion
Salt & pepper, hungarian paprika, just a hint of cinnamon (or nutmeg, or clove) Cayenne sometimes, not always just a hint.
Cook until veggies are done, whiz with your boat motor blender. Add seasonings and bring back up to temp. While soup is reheating either chop up some leftover meat, or make poached egg for protein. Sprinkle with cheese. When I use leftover meats, I sometimes put a dollop of sour cream on to instead of Parm/Rom cheese.
Fast easy, good.