I wonder if ADC and DAC that at EVAL-ADAU1452MINIZ can work synchronously ?
From your other post, it appears that you wish to synchronize a "click track" to incoming audio. This may or may not work depending upon the application you envision, as well as your timing accuracy need. The ADAU1452, the AD1938 codec (on the same eval board), and SigmaStudio can all simultaneously input and output disparate signals for ADC and DAC -- even though these inputs and outputs are sometimes shown as stereo pairs. However, the delays involved may exceed what your application will tolerate.
The AD1938 applies digital interpolation filters to both its ADC and DAC -- this allows you to input and output analog signals without providing your own brick-wall analog filters before and after the chip. These filters have input and output delays totaling about 1 mS at 48 KHz -- for the exact input and output group delays, see page 6 of its data sheet. The ADAU1452 may also have very short delays between I2S I/O and its core -- I don't know exactly how much, but these delays total about three samples in the ADAU1701.
So, there's a delay before the ADAU1452 knows an input signal is there, and another delay between your desired output signal and the DAC output. The delays match well between channels, so sometimes your application allows you to use this delay matching to your advantage.