I did a few more tests with this device:
First, linearity before and after calibration:
It seems calibration is already off by 1% again after the weekend but all in all I think this more than okay for a clamp measurement. I do not have a Tektronix or Fluke available right now, else I´d love to compare.
Then, I did a quick test about frequency response. It was done with a waveform generator feeding a 12Ohm-resistor and a scope measuring RMS on the resistor and RMS of the current clamp. The plotted value is the deviation of the measured current to the calculated current by Ohms law. Current level for this test was only around 60mA RMS because of the limit of the waveform generator.
I wouldn't give the values over 100kHz to much confidence due to the setup. But it seems this clamp is quite okay to measure RMS up to 25kHz and resolve current spikes down to the microsecond range. I´m quite happy with this result.
This frequency response shows that a separate AC calibration is not necessary. If you connect this clamp to a RMS multimeter, then the DMM cares about the "rectification". In the mains frequency range the deviation will be quite low.