Yes, you want to use a sharp drill and be sure to keep it running parallel. It may be worth making a contraption to help hold the drill still and mounting it on the crank case. The crank is quite hard and the bolt is soft so that should help. Once the core of the bolt is removed the thread can be removed with the very careful use of a pick and a tap. Making a left handed spade drill or buying a left hand flute drill and drilling backwards with a pistol drill might unscrew the bolt as soon as it frees up.
Alternatively you could try to directly arc weld, solder, braze or glue a shaped tool into the broken end after drilling a hole into it. I'm not sure how this could be done.
Failing that the safest thing to do is to removed the crank shaft and have a company use their spark eroder on it.