Maybe, maybe not. At the end of the movie Moneyball, we see Billy Beane fly to Boston to talk to John Henry, who compliments Billy on how little the A's paid (team payroll) for each win that season (2002), especially in comparison to how much the Yankees paid for each win. He then offers Billy a massive salary to come do the same for the Sox--which Billy declines.
This season we have seen not one but two AL East franchises field terrific teams--the Orioles and the Rays--with payrolls ranked 28th and 27th in MLB. Sabermetrics might have been involved, but the story line is that they have good minor league systems that produced talented young players who are not yet pricey free agents.
The Yankees and Sox, meanwhile, have plenty of pricey free agents who haven't delivered. The Yankees payroll is 2d highest in MLB and the Sox the 15th highest. Appropriately, the Sox have the better won-lost record.
In the middle of the AL East--the best division (based on won-lost records) in MLB--are the Jays with 9th highest payroll in MLB.
We can hope the Sox can win using the Rays/Orioles model, but they won't until they figure out how to assess and develop young pitchers.