Yes, free trade benefits the global economy, because it reduces prices everywhere. If one country can produce a good or service with less cost than another, allowing the more efficient country to produce that product frees up the people of the other country to do something else, and allows them to buy the product at a lower cost, saving them money, which allows them to buy other things, which increases sales and commerce. Lowering prices has a positive ripple effect that everyone benefits from when there is free trade.
Free trade is an extremely foolish trade policy. If taxes are not collected on exports, then the profit gained from exporting goods is lost. Tariff collection was the backbone of the American economy in the late 1800's and early 1900's. This alone should be proof enough that free trade agreements do not benefit anyone in the long run.