While it may provide a feeling of cool on the back of your neck, it really isn't going to do a whole lot to actually keep your body cool.
The device reportedly weights 3 ounces (85g) and can run for up to 90 minutes on a charge. If all of that weight was just the battery, using some of the best battery technology currently in mass production, you'd have around 23Wh of battery capacity, best case scenario.
Over a 90 minutes discharge, that's 15W power consumption.
The coefficient of performance in most practical TEC (peltier) implementations is between 0.4 to 0.7. So for a TEC operating at 15.3W of power input (again, ignoring the power used by the fan), will be able to "move" between 6 to 11W worth of heat.
The average human body dissipates approximately 100-120W of heat, at rest. This goes up considerably with exercise.
So very best case scenario... the device will help dissipate about 10% of your body heat, while you're sitting doing nothing. In reality, probably no more than 5%.
It may provide a pleasant feeling of coolness on the back of your neck but that's about it. You'll probably sweat just as much as if you weren't wearing the device.