I'm not sure if I understand you correctly, but no, the output current is very clean, as there is no high-current HF switching. If you neglect the S1-S4 "transformers", the IR21531/MOSFET gate driver part it is just a quadrupled full bridge forward converter, producing ~10V@5mA DC and operating at ~300kHz. The not shown filtering capacitance is the parasitic MOSFET gate capacicance, in this particular case in order of 20nF each. At this frequency it is more than enough to provide stable 10V gate voltage, which, under the above assumption, means that the oscillator IC is working hard to keep all the four MOSFETs constantly on.
The trick is based on my discovery that about one ampere-turn is perfectly enough to drive this particular ferrite into saturation. In essence, the beast is magamp-controlled, with the high-current MOSFET source pin having dual role, i.e. it is also the single-turn control winding of a saturable reactor. :-)
If the body diode current is high enough (i.e. ~800mA+), it saturates the S1/S2 or S3/S4 toroid pair and the reactance of the other winding disappears, effectively connecting Tr2 or Tr3 to the oscillator and thus producing gate voltages on the appropriate MOSFETs, which shorts the conducting body diodes and reduces heat dissipation. Then it is self-sustaining. If the current decreases below the saturation threshold, the magamp cores reset and turn off the MOSFETs even more. And since the magamps are not voltage, but current-controlled, the entire device doesn't care whether there are filtering caps or not, exactly as a diode bridge does. In order not to inject HF into the output/mains, there are two oppositely connected magamp pairs instead of just one, i.e. 4 small control toroidal cores in total.
If you perform a bit more detailed analysis, you'll discover that this mode of control is inherently stable. In practice I wasn't able to devise a crazy enough, yet realistic scenario to derail the control circuit, but to be at the safe side, there is the T5/T6 protection AND gate with the transistors having much lower threshold voltage than the main switches. If somehow both halves were to conduct simultaneously, the oscillator would be stopped, resetting the synchronous rectification control system.
Best regards, Piotr