face up disrupted counters are removed BEFORE you flip the face down counters, so no, you can’t add a face up disrupted counter to any new face down counter.
In fact, a disrupted counter never adds up with another counter. So, if a vehicle has a face up damage counter, and in another turn it gets 1 hit, than you put a face down disrupted counter that will get flip during the casualty phase, and the vehicle will have both a face up disrupted counter AND a face up damaged counter, but it won’t be destroyed.