Oliver, Prof. Gerard Nihous of the University of Hawai is considered the authority on the amount of energy that can be produced with OTEC. In his latest work he puts that potential at 14TW or 250,000 100 MW plants. This is what we currently get from fossil fuels but others have put the potential as high as 25 TW. This energy will be produced in the tropics and will require an energy carrier like hydrogen to get it to market. (Don't forget much of the world's oil and gas comes from the Middle East requiring transportation over equally long routes.)
Also that tropical heat is driven by the second law of thermodynamics towards the poles where it melts the icecaps.
A group lead by Greg Rau of the University of California Santa Cruz have developed a technique for producing "supergreen" hydrogen by the electrolysis of sea water that removes and stores atmospheric carbon dioxide while generating carbon-negative hydrogen and producing alkalinity, which can be used to offset ocean acidification.
Your wikipedia link points out the thermally efficiency of OTEC has a theoretical maximum of 6 to 7 percent but in reality existing efforts are half that.
A 2010 NOAA study found the upper layer of the world’s ocean was storing enough energy to power nearly 500 100-watt light bulbs per each of the roughly 6.7 billion people on the planet - http://www.noaanews.noaa.gov/stories2010/20100519_ocean.html . I make this to be about 335 terawatts.
The thermal efficiency of the heat pipe design is about 5 percent so to produce 14 TW with the design you would have to pump 280 TWh into the deep and the conversion would bring the benefit to 294TW or just about all what is currently being added. And with the heat pipe you pump zero water from the depths because only the working fluid vapor is moving from the surface to the cold sink, where it is condensed and then pumped back again. This requires the movement of about 8 m3 of ammonia for a 50MW plant as opposed to about 150 m3 of water every second. The parasitic losses of this system are about half of the other.
There are a lot of climate and energy wins with such a system.