No. Ocean engineer here. Currents have a lot of power (not energy, but power), but unless you mean the whole Gulf Stream, or a very long time period, the energy of the world's nuclear weapons is greater still. But it's kind of hard to argue with someone that isn't consistent with units.
Two ACs arguing about the energy content of ocean currents vs energy content of nuclear weapons, with neither one putting up a single number to back themselves up. Tsk tsk.
Lets see: total world nuclear arsenal currently about 6400 megatons, or 2.7 x 10^18 J. Gulf stream volume 150 million cubic meters/sec at Newfoundland (1.5 x 10^11 kg/sec), speed 2 kt, or 4 m/sec. Kinetic power of stream = 1.2 x 10^12 J/sec. Number of seconds for the kinetic energy of the Gulf Stream to equal the nuclear arsenals = 2.25 million, or 26 days. Is that a "very long time"?
But wait, there's more! The heat transport of the Gulf Stream is 1.2 x 10^15 J/sec, a figure 1000 times larger than its kinetic energy, so the time for the Gulf Stream flow to transport a "world nuclear arsenal" worth of energy is only 2250 seconds, or 38 minutes.