I have this recipe for lasagna that says to brown all the meat(beef and sausage) first, then add the tomato sauce and cook longer. If I add the tomato sauce to the raw meat and cook it all together, would it be safe?
JenyEma nailed it. As a side not, if you combine sauce to ground beef, but it moderate amounts, you can make some pretty interesting, and flavorful meat loaf mixtures.
Safe? Yes... Good? No! Hi! Marco here.
Browning correctly will give taste to the meat: the Maillard's reaction combines amino acids and sugars when the meat is exposed to temperatures between 140-180° (see http://en.m.wikipedia.org/wiki/Maillard_reaction). Seedling the meat at that temperature, the meat will remain soft, it would dry and harden instead if mixed to the wet tomato sauce or purée.
Also seal the meat with fat (oil or butter) and choose cuts with fat: it will give flavour and keep it soft.
Well... This is the long boring explanation. The quicker answer would still be this: NOOOOOOOOOO!
Bye! I hope I've been helpful somehow