Hi Stephen,
I am assuming you are using the microphone circuit as per the datasheet with the electret microphone which can support the recommended bias circuit. If that is the case then, connecting single microphone to two inputs can be wired to work with some redundancy.
So if you plan to do it then connect the microphone bias resistors as usual but add 2k to 4kohm resistors in series to each of the inputs to ADAU1977 from microphone terminals. Please remember this is valid only for the microphone biased as shown in the application circuit of the datasheet.
Thanks
Rajeev