Yes, (unsurprisingly) if you force the CSRF cookie to be unreadable
from javascript, then you will not be able to use javascript to
extract the CSRF token from the CSRF cookie when you submit an AJAX
request.
The requirement in order to use CSRF is for your AJAX submission to
include a CSRF token. This means you must insert the token some other
way, eg by including a hidden element in the form or page that
specifies the CSRF token, and will be included when the form is
submitted via AJAX, or extracted from the page and sent with the AJAX
request.
Cheers
Tom