Since I am hard of hearing, I missed the origin of the debris field that the hit them.
It was said to be from the Kessler Syndrome, which is a real concept: as we reach a critical density of debris in orbit, collisions will become more frequent, generating even more debris that generates even more collisions. Whole regions of orbit could become almost unusable because of the debris hazard.
But it doesn't happen
that fast. It develops over years, especially after rare but spectacular collisions like that between Iridium 33 and Cosmos 2251 generate large amounts of debris. But the debris is mostly small and spreads out along the orbit; it doesn't travel in close groups of big visible chunks as depicted in the film. If one ever hit, it would be as if somebody shot you with a very high powered sniper rifle with (most likely) a very tiny bullet. And you wouldn't see it coming.
There are arguments that a Kessler Syndrome has already started in certain low-earth orbits, particularly around 800 km. The one in
Gravity was said to originate in geostationary orbit (I think - somebody correct me) which is far less likely, would not develop as quickly as depicted, and would not send debris so low.
And you wouldn't see it coming, at least not in the way depicted. You might have warning of the larger chunks since they can be tracked and cataloged on the ground, and the ISS astronauts routinely dodge these things (if they have time) or hide out in the Soyuz (if they can't). But most of the objects are too small to be seen with current sensors, and that's what people are most worried about.
As an analogy, you wouldn't say the volume of space including an active battlefield is "crowded" with bullets in the sense that they mostly fill the available volume, nor are you likely to see any of those bullets in flight with your own eyes. But you sure wouldn't want to travel through there.