Uh, nope. The classic Beck circuit produces AC exactly the same way early AC generators did. In terms of the nature of electron flow, it is the same as a wall outlet with one exception - there is a brief time period in each half-cycle when the circuit is completely disconnected from the person. this happens every time the relays change state. Other that that, the BBBE definitely IS AC. Square wave, sine wave, blah blah - under it's influence, electrons flow in *alternating* directions. That's the A in AC. Ground one end and look at the other, and it will appear to go above and below ground, just like a wall outlet.
More about adding an output diode (won't do what you want), Loyd, etc. later.