Hello Fernando,
SigmaDSPs do have a "safe read" feature, allowing you to read from the DSP core rather than from RAM. This is necessary because while the RAM is busy with I2C / SPI requests, its contents are unavailable to the core -- thus the pops and clicks. Really this is the main reason for safeload write, which forces RAM updates to handshake with the core. The stuff about needing to have all the biquad coefficients update together is also true, but really it's more fundamental than that. Even single-parameter writes to an unconnected DC source, for example, results in audible pops. As you're finding out, read requests also tie up the RAM, thus they too cause pops.
Instead of reading from RAM, use the data capture feature described on page 38 of the ADAU1701 data sheet. This accesses internal DSP core registers where you can gather the data you need. It's the method that SIgmaStudio uses to access data through the USBi for Readback and Real-Time Display functions. BrettG (I miss him!) wrote a tutorial on its use, found at Using hardware data capture (trap) registers with the DSP Readback cell (AD1940, ADAU1701)
Best regards,
Bob