You would have to assess this on a per-model basis. In a lot of assisted knives, the torsion bar is what holds the knife closed, so if that were to break, the blade could swing open freely at any time.
The knife would still be completely usable (open and lock-up solid) if you needed it, but I wouldn't put it in my pocket and go jogging.
If you wanted to prepare a knife in advance for this possibility, you could set it up with a ball detent (which is what keeps almost all knives closed).
If you were really concerned about this, you could get one of the rare models that allows the assist to be turned on and off. As these are obviously designed for non-AO operation. Off the top of my head, the Kershaw Cyclone and I believe some models of SpeedBump have this feature.