Yes - the marriage would be recognized in BC.
No - you can't just move to BC and live/work there after getting married. Read here for what steps you need to take next:
http://www.canadavisa.com/canada-immigration-discussion-board/spousal-sponsorship-t46995.0.html
Note that you are also posting in the wrong section of this forum. Try the Family Sponsorship section instead:
http://www.canadavisa.com/canada-immigration-discussion-board/family-class-sponsorship-b5.0/