ADS8586S: Does an end of conversion reset the read out register address?

In my application I readout all 6 channels after each conversion (when BUSY goes low). Sometimes, due to timing limitations, the system will make a few additional reads (1-2) after all the channels have been read out but before the next conversion starts. Will channel 1 be the first channel output on the first read after the next conversion ends or does it continue on from where it left off during the previous sample readout?