It may be that I discovered this information too late, but I tried the alum solution repeatedly on my latest canker sore (haven't been able to talk or eat pain-free for 5 days now) and it seemed to make it a little worse. It certainly didn't help, although it wasn't as painful as some of the posts here warned it might be. I would have to vote Nay for this one.
Alum is a form of aluminum. Oral injestion of aluminum can cause canker sores. Do you really want to do that? The reason it works may be the same reason that the mercuric ointment my mom used to put on my rashes ( I later found out that I was mercury toxic) got rid of my rash. Apparently, it makes it go deeper into your body, thereby getting rid of the eruption on the surface.
EC: More about this here: http://www.ochef.com/1080.htm