It is not as clear cut as that, otherwise every prosecution for driving without MOT would be accompanied by one for driving with no insurance. This is not the case.
If there was an accident, the insurer may decide not to pay out if the car has no MOT. It depends on whether or not it was generally roadworthy. Note she says it is the car's first MOT - so it is 06 reg and unlikely to be a total rot box!
Driving without an MOT is a non-endorsable fine of up to �1,000.
It does NOT automatically invalidate insurance i.e. the police will not stop a car with no MOT and do the driver for no insurance.
Again, I am not saying she should do it by any means in fact I advise against it - you should always drive with your vehicle's documents in order.