you can add raw garlic to sauce, but if it's bitter and sulfur-y, you'll get bitter and stinky sauce. some people like the flavor, but i don't. also, the more you cook your garlic, the more you have to use as the flavor mellows considerably.
one more thing: don't be stingy with the olive oil when carmelizing the garlic and onion, sweating veggies, or browning the meats. it adds flavor and "viscosity" to the sauce. some people even like to finish their red sauce with a drizzle of very good quality evoo.
btw, in goodfellas, the reason the razored the garlic was so that it would cook using as little oil as possible. they were in prison
another tip: avoid using most "fire roasted" canned tomatoes. they contain skins (a skin-less tomato never chars), which are unpleasent in sauce. they curl up and become little spikes.