Nope. It doesn't affect stars. Only playing a level normally let's you get three stars. The Mighty Eagle requires your to get 100% completion instead, which is destroying everything on the screen with it. You can also use it to skip over a level if you get stuck since it's kind of of hard not to win when you launch a 'bomb' that takes out half the screen.
No it's if your rlly stuck you have the eagle and take the level out plus you can collect the feathers in all 45 levels ;-)
It is worth buying - not only does it help you get past hard levels, but it basically doubles game play for each level by giving you a destruction level where you need to aim the eagle. 100% nets you a feather for that level. Some of them are really hard to figure out.
Generally it's not fun to play a game after the game lost challenging. Personally I think the Mighty Eagle is not a necessity to buy as it eliminates the difficulty.