I will also have to add my "Eye" to this experience with drilling out bolts as this has been my experience as well. I have had some good luck with being able to drill out a broken bolt, but having a Mill or a very high quality drill press will improve your chances. Be very careful to not break off a tap in the hole. Sometimes you can get the tap to catch the remains of the thread of the bolt and they you can work it out with a sharp probe. Careful work, and not always the result you want. This is why I went to the welding method I was talking about in my other posts. By building up weld onto the broken bolt or stud, you are not only heating the bolt, you are giving you something to grab with a vice grip. Even if it breaks off a second time, do it again. A welder is really one of your best friends in restoring these old motors. Learning to TIG weld was a real asset in getting the results I needed.
In the most recent restoration I have just completed, ( A 1972 Mercury 4hp.), it was not broken bolts that was the issue, it was broken aluminum. These motors had a really nice shallow water drive option. The issue, as it had been a rental motor, both of the aluminum bosses in the swivel bracket had been broken off. Also, the skeg had the usual damage and missing section. Being able to return these items to as new or better condition could not be done without welding. If you can weld, great, otherwise make friends with one! A case of beer can go a long way in saying thanks for your help!