Interesting thread, whilst I don’t own a 500x anymore to check, it did have FCW.
If you’d have asked me I would have said it would bring the car to a halt, but thinking about it, all I got was a audible tone followed by a jolt from the brakes. If an obstacle was in the way I would have been applying the brakes myself at that point so would have stopped anyway.
On a couple of occasions the system thought I was going to hit something, like a parked car and it would stamp on the brakes, but then release them. As a driver, my reaction was to be on the brakes at that point wondering what the hell was going on.
I need to check my current car (Volvo) to see what it does. The thing is of course that if you’re paying attention, as you should be, you’d take over control anyway and the car would work with you to assist in stopping as quickly as possible.
It would be a very brave driver who wouldn’t jump in and stamp on the brakes when something appears in front of you.
Only way to be sure would be to find a brick wall and drive at it and see what happens. Make sure you video it so you can put it on YouTube though as I wouldn’t trust it to work.

All these things are
aids for the driver and should never be considered a fail safe. Look in the manual and there will be lots of get out clauses.