Is this current measurement solution okay?
That CT only is rated to be accurate down to 50kHz. If you have 50/60Hz, it won't work. A CT rated for  accurate operation at 50/60 Hz will be much bulkier.

The bridge should give you peak 8.0V without the capacitor (12A/70 = 0.172A = 0.242A pk * 33R = 8.0V) minus 5% or so average ripple at 50Hz. The CT may not be capable of the burden including the bridge - but looking at it- the bridge introduces two diode drops so it adds to the burden, but it's specified for 70R so 33R + 2 diodes should be okay.

D1 will just ensure you raise up Vcc- you're asking Vcc to sink around 200mA.. It might work with a series resistor from the RC depending on the resistor value your ADC can tolerate and what other loads are on Vcc.