The VOT tolerance is based on the accuracy of the VOT signal and the expected VOR receiver ability to resolve the test signal. It is completely separate issue from the inflight course line accuracy which includes such things as Flight Tecnical Error-- how accurately you and I can track the VOR signal, how accurate the signal is given conditions, tolerance of presentations, etc.
Yes, the flag will appear with an invalid signal, but that does not necessarily mean when the plane has flown past the service volume of the VOR. Fir example, a High VOR has a service volume of 230nm, but you will not get a flag at 231 nm. Coasting out overwater at FL450, it is common for the VOR and DME signal to stay until around 270 nm or so.
GF