should this combination of a ADA4666-2 and a ADC-converter work?
You are operating the photodiode with 0V reverse bias the way you've shown it. This should be fine but if you wanted to you could disconnect the photodiode from VREF and apply a reverse bias in order to reduce its capacitance. However, ADA4666-2 is happy either way with the schematic you've shown.
You're throwing away some ADC input voltage range because you cannot swing below 1V at the analog input. I assume you're ok with that.
With the components you've chosen, you can expect a -3dB BW of around 1.7kHz.