Sure he does. He has almost as much experience working in baseball as AA has years on the Earth. He's been the GM of a Canadian team and two other teams in the AL East. Before that he was a director of player development, and in the middle he dabbled in amateur athletics and owned and operated a sports academy in Mass. and was owner/president of some summer collegiate team.
He's more basebally than most Presidents, but teams vary widely on top end organization. Some teams have a pure business dude in the President role, others have a former GM and a true baseball guy. Others split the role - the Cubs have a President of Baseball Ops (Theo) and President of Business Ops.
With the Blue Jays, it makes sense to have a guy with a ton of GM experience in different organizations in the President role. They don't really need a pure "business" guy because there are already countless suits above the team in the ownership group.