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The other thing you can do if your CAREFUL is to take a long flat-head screwdriver, place the head on the bolt of the pulley and your ear on the "butt". You can hear the difference between a shagged bearing and a good one.Probably a rough bearing in one of the serpentine belt pulleys - remove the belt and spin pulleys by hand. If they fail completely the car will stop.
Can't see how it would - the reason your car stops if a pulley bearing fails is that it throws the fanbelt off and you lose your waterpump and the car will boil very quickly - if you don't stop immediately you stand a good chance of seizing the engine. Re your miss I'd do a fault code check as your CAS may be failing and you are getting an early warning. "How to" is attached:could this cause the car to cut out for a second but turn back on automatically straight away coz my car did this yesterday? didnt even have to touch ignition or pedals or anything, just went out and then straight back on