With any sport during which you attach your feet to long, inert objects, and go through precipitous terrain, covered with substance and/or hidden snags that could halt progress of those objects, while your body continues motion, there is a change of gnarly wrecks. In other words, yes. But since generally only the front of your foot is connected to a binding, you have some more movement, compared to downhill. Unfortunately that binding generally doesn't come loose when you fall, in fact if it does, you must be in a big wreck.
That said, a lot of cross country can done on fairly decent trails, but then the interesting places often are at the far end of trails that aren't often used, across more difficult terrain, winding, etc. On the upside, the pace while trekking around on XC skis is usually not that high, especially not if you are breaking trail.
I tried an alpine touring set-up just the other day, and unless you get to steep terrain and want to incorporate downhill, I'd stay away from it. It is heavy and slow. But when equipped with full-length skins you have some serious grip even on quite steep and slippery terrain. If I had to make a choice right now, I would go with a good XC set-up, with good insulated ("plastic") boots, metal-edged skis, wide enough to provide buoyance in deep snow. I use "plastic" boots in my racing XC set-up, and have been for years, and they work well, even though the area around the metal bar up front can wear down quickly if you walk on anything else than snow.
Frans