The gulf stream maxes out at about 5 knots, but that does not mean it has that speed everywhere. For a surface vessel without much draft, wind probably has a more significant impact than currents and he'd be very dependent on the changes in the weather. A stiff breeze from the north could easily end up with him further south than he started.

And of course, the further out you go to try and pick up the gulf stream, the further you have to go to get back to shore.