Having a diode before the burden resistor should not be a problem. Yes it means that the system won't have a well defined lower cutoff frequency (or time constant), but generally that cutoff will always be well below your bandwidth of interest, so it shouldn't have a noticeable impact on performance.
When using a diode before the burden, it is wise to provide a current path in the reverse direction, which can be done with a reverse clamping diode directly on the CT output.