Google will not see 403 unless Google follows the link and index your site and Google never does it that way or else it will never end indexing any given page.
So if I am on site A - and finds links to site A1, A2 ... A10 on Site A, I will not follow each link but I will make an index of Sites A and then add the links A1 to A10 to be visited and then visit each of those links and index. (Assuming Site A and A1 to A10 have one page for understanding)
So Google's bot will not be visiting Site A1 with referral from Site A or Page A
So Google will always be able to index those pages but users will not.