It can be done! But I wouldn't want to try it.

Interesting article at http://www.cbc.ca/story/canada/national/2006/07/22/bear.html

A man in North Ontario was on a 12 day canoe trip, alone except for his dog. They were attacked by a bear, and he killed it with his hunting knife. He and the dog were both biten, and he had to paddle for an hour until he found some fellow campers with a satellite radio. Sounds like a small one (only 90 kilos) but I still have a special place of respect for anyone who kills a bear with anything less than a 30-06 rifle.