Yes, for the Mexican definition of "storebought" which means "grown by Juan Carlos on his farm in the next state over and trucked in two days ago in his clapped out 1987 Ford Ranger with welded suspension."
Merely washing your industrial ginger might not be enough. Best if you can find a piece at the store that is already sprouting. Maybe the organic section, or the farmer's market would be better. Dunno.
You can chop it into small sections to grow a lot of plants. They don't like the full sun here, but will probably grow fine in an open field in Canada. Make sure the soil is well-drained, and they get plenty of water. Their natural habitat is sandy stream banks.