It's a variant of Kick the Dog (http://tvtropes.org/pmwiki/pmwiki.php/Main/KickTheDog)
It CAN work, and I suspect for parents, it's a pretty easy button to push. I had someone close to me die from cancer, and despite the fact I KNOW it's cliche, everytime I see the hospital scene with the beautiful girl passing away to the blip of a monitor, it still gets me.
That said, it works better if we've been given a chance to care about the character. If, for example, Shep had actually talked the kid out of the ventilation duct and escorted him to the shuttle only to see it blown up later, we'd care more. Or take the girl (name escapes me) that Morinth killed in ME2. We get a chance to listen to her diary and learn from her mom that she was a creative, but introverted, artist. That actually pulled a heartstring, but not in a cheap "Oh look, pretty girl is dead" way. She was a real character, even if she never appeared onscreen.