Yes my understanding has always been a permanant airbag warning light is a fail on the m.o.t but I know a fair few who have passed with it like that.I think a lot of places may if the car is otherwise in good,solid condition write it up as an advisory rather than fail you on it but if the car has a number of problems then it'll be flagged up as a fail too.
I know it's not something many would not like to believe,admit or even imagine but I do feel there's a certain degree of psychology at play when dealing with m.o.t testers.Ok I'm sure everybody will say there should definitely not be,that it has to be clear cut,wholly objective.Black and white.Until robots or algorithms test our cars it will be done by humans and humans are,well human afterall lol