What that battle did, though, was make the Patriots think that they could--at that point--meet the Brit regulars on the field of battle (they dug in like crazy at Breed's Hill and did not march in line against the Brits). This set them up for the rout that was the Battle of Brooklyn more than a year later.
They would need the discipline and training that von Steuben brought to the Continental Army to be competitive with the Brits and Germans.