Would this be a dangerous impeller to use for a drone?
I know those things as squirrel cage blowers. As the video says, they are a good choice if you want to move a moderate amount of air without exposing rotating blades.

Impeller, by the way, was initially the word for a sort of airscrew that is moved by the flow. The small thingy in the nose of the Me-163 rocket interceptor was an impeller and needed for driving the plane's electric generator. Unfortunately, this word has recently been abused to mean shrouded propellers. 

The proper name for those blowers is "centrifugal fan", and I will continue to use this word for the remainder of this answer.

As @pericynthion says in the comment, air pressure is less of a concern than centrifugal loads. Basically, the blades spin air around and hurl it to the inner housing of the blower, increasing pressure when the kinetic energy of the swirling air is converted to pressure as the air slows down. If we assume that air comes to a total standstill at the housing (which it doesn't, otherwise the blower would choke), the maximum attainable pressure is determined by the radius of the cage $r$ (in meters) and the rotational speed $\omega$ (in rad/sec) of the blades.
$$∆p = \rho\cdot r\cdot\frac{\omega^2}{2}$$
For a 20 cm blower spinning at 3000 RPM this would be 5.9 bar. The centrifugal acceleration $a$ on the blade would be
$$a = r\cdot\omega^2$$
which produces 1000 g with the same parameters.

To give you an idea about the efficiency: It is generally desirable to accelerate a large volume of air a bit rather than to accelerate a small amount of air by a lot. Therefore, helicopters use the largest practical rotor diameter, so they can capture as much air as possible for lift creation. Centrifugal fans cannot enjoy the same luxury and can only use the air which enters them from the side. As you can see from the two formulas above, your ideal centrifugal fan runs at a low speed but has a large diameter for the best ratio of pressure over centrifugal loads.

If you build them without regards to the loads, yes, those centrifugal fans can indeed be dangerous.