The DC signal will be the peak voltage.
Actually true for capacitor input filter, whihc this is, minus the diode drop, which the op amp cancels out, so its nearly the ideal case of DC = AC peak.
A possible problem is now that peak may include noise. In this naive version of ideal rectifier the op-amp spends most of its time in "saturation" where the inputs are unequal and it wishes it could go below gnd (neagtive). The consequence is when positive peak comes along, it takes a while for op-amp to de-saturate and get back into the linear mode it was born for. It is slow to responde.
So if a very short pulse, motor brush noise for example, comes along the op-amp cant de-saturate quick enough to turn on diode and pump up the capacitor to follow it before its gone. This is a good thing as you probably want the real current, not the noise.
But in the case of AC wave with smooth sinusoid top, the op-amp is hopefully got plenty of time (milliseconds is an eternity for them) to de-saturate and push the capacitor to follow the input. A noise pulses near the peak of the AC when the op-amp is already de-saturated and in its linear mode might indeed get included as "peak AC load current".
In the case of noise near the AC peak we are totally dependent on the R-C to the left of the op amp to prevent noise from creating a false reading. I would recommend testing at first with a simple tungsten filament light bulb (are they still legal?) or other purely resistive load that draws a sine wave current. Complex currents like Dimmers will be more tricky and home electronics like PCs, audio, video, and even the CFL bulbs mostly draw pulses of current only near the AC peaks.
Real power is the integral (area under curve) of product of yellow and red curves. Since the current (red) is narrow the peak reading overestimates the real power. The popularity of these type loads is becoming a serious problem for utility companies.
Motors with mechanical brushes are the noisiest (drill, blender, vacuum cleaner) but I disnt find a good picture.
The CT will pass many times the AC line freq, which is near the BOTTOM of their useable freq range. Transformer manufacturers do this to save iron and copper, to make the transformer smaller, lighter and cheaper.
More sophisticated instruments digitize the actual waveform for voltage and for current, they compute the lead or lag of phase to separate "real current" from "reactive current", they "integrate the area under the curve" for complex waveforms and despite all the fancy stuff they still fail to read accurately when "crest factor" is too high. (google the terms in quotes for more info). Besides beign waaay too much processing for an Arduino, its a complicated way to do not very much better than the simple approach.
So just keep in mind load current "peak" may not be pure sine wave. An oscilloscope will help. When strangely high readings are seen, go back to simple resistor load and make sure the numbers are what you expect. Play with the RC values on the left side to filter out "peak noise" for ugly current waveforms and I believe this simple approach will end up working pretty well.
Thanks for makin me think on AC current monitoring with CTs, its on my list of projects to do some day. If you find a great discount on CT prices, let me know!