I know that we have the option of listing "NA" for employee loans in order to protect their privacy, but is the same option available if the loan is to a Board of Directors member?

I haven't run into this yet, but it seems as though you can based on past discussions. Of course, it'd be great to find something "official" to rely on:

https://www.bankersonline.com/forum/ubbthreads.php?ubb=showflat&Number=1727132

There should not be any issue with using NA for board members for HMDA. The situation is identical to employees, insiders of the bank.