Generating thermal noise from a resistor
you got popcorn noise on front end OA too.. no longer random

OP Amps generate Pop Corn noise unlike thermal brownian motion random noise, so your assumption was invalid. THis works for microwave noise range but not for audio frequency range unless you use low noise OA that is lower than a resistor.
Hence your design will not create random number gnerator from the time domain bias of pop corn noise in active parts.