Running (even a marathon) is definitely possible for a patient with MG who is in remission or has a very good control of his/her disease.

Walking a longer distance than you should (which can be no more than 200 meters) can be dangerous for a patient with significant uncontrolled MG.

Only you know what your physical abilities are at a given time.

One MG patient can go from being on a respirator to running a marathon.

Another MG patients can never walk more than a short distance.

It depends on the nature of the illness and the way it responds (or doesn't respond) to treatment.

As you well know a trained marathon runner will never run at a speed which is beyond 70% of his maximal ability.

The elevated white cell count can also be the result of over-vigorous exercise.