Why escaping an American port did not evade the British blockade

Did the protection described for British trade also apply to American merchant vessels running the blockade?

No. American merchants also faced British ships far from American ports, often near the other end of their voyage.

The blockade of American ports created one obstacle for merchant shipping and helped contain American warships. Merchantmen that got through still had to complete the rest of their voyage. British ships operating far from America posed the larger danger in this assessment, with captures often occurring toward the other end of the route. Reaching open water therefore did not mean that an American merchant ship had passed beyond British naval reach.