Can I use MAX11201 with 1.2V reference voltage?

Yes. MAX11201 can accept a VREF input from 0V to VAVDD (analog supply), where VAVDD can range from 2.7V to 3.6V.

The analog input voltage in the MAX1201 datasheet is restricted from VGND+100mV to VAVDD-100mV according to Electrical Characteristics Table. However, in the schematic shown in Figure 6 of the datasheet (Rev 0 6/10), AINN is tied to GND. Is there any issue

There is a built-in input buffer in the MAX11201. Therefore, the input voltage is limited to the range of VGND+100mV to VAVDD-100mV. The connection between AINN and GND in figure 6 is incorrect, and may result in a larger measurement error. It is recommended to place a resistor between AINN and GND to "raise" the input voltage of AINN such that the input voltage can meet the requirement of VGND+100mV.