Yes, and it does on every flight since it's used to return things from the space station back to Earth. However an abort system also needs something to move the capsule away from the (probably exploding) rocket when something goes wrong, which is typically a strong and short-firing rocket on the capsule itself.
In this particular case, it sounds like Dragon survived and probably could have been recovered using the parachutes, but they weren't armed since survival without an abort system isn't something they really try for. It would be interesting to make the attempt, but not informative for manned flights since those will have a proper abort system.
It would be interesting to know if they can remotely trigger the parachutes - i.e. in this case after it had fallen a ways they could have triggered them - even just to see what would happen.
Yes, it seems likely that the capsule and at least some of the contents could have survived if they had opened the parachutes on descent. Of course, I don't know where it would have landed or how long it would have taken to get a ship out there or.... Anyway, I imagine it just wasn't in the plans for something like this.
In this particular case, it sounds like Dragon survived and probably could have been recovered using the parachutes, but they weren't armed since survival without an abort system isn't something they really try for. It would be interesting to make the attempt, but not informative for manned flights since those will have a proper abort system.