I don't think it would cause the car to stop. Actually if you think about it, it would cause the car to *not* stop!
You sound like you're not entirely certain that your dealer is competent to diagnose the problem, so there's no harm in going to get a second opinion. If the problem caused all of your warning lights to come on and the engine to quit I would guess that the BAS/ESP light coming on is just a symptom of a larger problem.