Note that this circuit will not have the usual problems with the diode drop affecting the measurements because the current transformer secondary will look like a very high-impedance device. You _will_ have to take the diode drop into account as John described, and the diode voltage will appear (attenuated by a factor of 200) at the transformer's primary leads.
You could "fix" the RMS vs. average absolute value issue by using an RMS to DC converter, but accurate ones are expensive and hard to get. You could also fix it by sampling the instantaneous current with an ADC (replace the cap with the ADC inputs) then computing the RMS -- but that's a lot of effort unless you're going into a microprocessor anyway.
I'd probably just assume a sine wave and apply the right conversion factor to read RMS, or I'd just label the voltage "average absolute". In either case I'd make sure that folks didn't think it was _true_ RMS if they looked at my schematics.