Short answer is no.
WP requires some permission set capabilities of the taxonomy to add terms. Since the user is not logged in they have no permissions. I’m not 100% sure what capability this is tied to, I think it is ‘manage_terms’ and by default this is tied to the ‘manage_categories’ permission.
It may be possible to use the user_has_cap filter to allow a logged out user to have this permission, but I can find no specific information on this. I would start digging deeper here.
