From what I can tell, it should react to a lot more than 5 minutes of vigorous wrist exercise. I lift and throw boxes and palettes for hours a day and I can seriously imagine keeping my phone well-charged if I had one of these. Not that I keep every app on my phone actively running to be in any danger of it expending all its charge in a workday, anyhow.
I can't.
Without going into the details of how much energy you use for loading boxes, we can simplify the matter simply by looking at caloric intake for weight maintenance.
An iPhone 5S battery has about 1440mAh, at 3.8V.
If you are maintaining weight at 2kcal/day, that corresponds to roughly 2.326Wh, which would give you 612mAh at 3.8V (2.326*1000/3.8). Or not quite half.
If you did nothing other than convert food to electrical energy, (at 100% efficiency) you would need to be eating along the lines of about 5kcal per day, to completely charge the battery.
The supposed discharge time for usage is roughly 10 hours, we'll bump it up to 12 for ease of calculation. Your shift time is probably somewhere between 6 and 12 hours, so we keep it at the boundary zone.
As a basis for the example, if we take the 5kcal/day number, and evenly divide it through the day, you'd be back to about 300-600mAh per shift, at 100% efficiency.
Now, let's look at that efficiency number. Let's assume the body is extremely good at converting caloric energy into mechanical energy (90%) rate, and that the band is very good at converting mechanical energy into electrical energy (75%). We're already looking at about 68% efficiency of the system, so you are looking at about 200-400mAh as an upper bound.
Except we are looking at caloric consumption of the body, not of the exercise itself. And the exercise is highly dependent on the mass of the item moved plus the mass of the individual, whereas the charging capacity is highly dependent on the mass of the charger itself and the relative motion(let alone if it is specific with regards direction).
And that doesn't go into the efficiency losses in the charger charging a battery, to charge another battery.
To put it broadly, I'd be surprised to see a design that could capture more than 50mAh in a day, and store more than 200mAh total. At that point, you could argue that it could serve as an emergency powerbank for your phone, in case you needed to charge it from being dead.
