Any thoughts on applying this principle to an AUV (autonomous underwater vehicle) ? if the power source is a battery, would its efficiency be beneficial to that of a propulsion system?
Dyson fans are NOT efficient (despite claiming otherwise). They emit about 1 gram of high-speed air for every 10 grams of air accelerated. Sounds efficient, right? No!
The Dyson fan is analogous to throwing a 1kg dart at 10 m/s toward at a 9kg target sitting on ice. The resulting dart+target has a velocity of 1 m/s (momentum conservation). However, the dart contained 0.5*1*10^2 = 50J of kinetic energy, but the ensemble ends up with only 0.5*10*1^2 = 5J of energy. The "missing energy" went into making a hole in the board and heat.
Your boat have the same issue. In fact, using a "multiplier" does not increase the thrust over a simple jet, since the momentum is the same. Thus it's better to push more water at a lower speed. When a boat is traveling at a constant speed, the propellors don't actually push the water backward all that quickly. There is no wasteful high speed jet.
However, regular fans are probably inefficient also because they use low quality parts. At $200, Dyson makes up for the mechanical inefficiency with better motors, etc.