If you are anemic, yes. But not everyone gets low potassium when starting B12. Most people do not get enough potassium daily anyway! I've known people whose teens and young adult children end up in the ER with low potassium! If a person uses diuretics alot, they can end up with low potassium, and magnesium as a side effect. There is one type of kidney tubular acidosis that wastes potassium over time. People with low magnesium often have a corresponding low potassium, as it seems they are connected somehow in the body.
There is also a genetic syndrome of low potassium:
http://en.wikipedia.org/wiki/Bartter_syndrome

Our red cells have a lot of potassium in them. So when red cell production suddenly increases, they will rob the body for potassium until that synthesis becomes more normal. Some people with low B12 have poor red cell production, but that would show up on a CBC testing panel. Other people do not show the anemia, until late in low B12 situations. So it is hard to say who will or will not see a sudden dip in potassium levels.