Yes, it's possible to break a pair. Heck, you can break anything if you try. But I think it very unlikely if you're just using them for cutting.

They all seem to be made of some sort of spring steel. The cheapest, thinnest ($2) ones will "dive" under heavy cutting -- the scissor halves will move apart rather than cutting through. But even then, they come back together. The better quality ones ($5-6) can chew through quite a bit of stuff; you can gently tighten the rivet and resharpen them as needed.

I've found crash scissors quite useful in a number of situations. For air travel or locations where all sharps are forbidden (schools), crash scissors are acceptable and accomplish a lot of tasks. I even use them to cut up oil rags in my shop; I have ten knives available, but the crash scissors are faster. And nothing is better for those d@mnable blister packs that everything comes in these days.