Q:

See Org Mode links in Org Mode comments

If I have an [[Org Mode Link]] and then make that line a # Comment [[Org Mode Link]] the fontification changes and I can no longer tell that it is a link. Can this behavior be changed?

A:

Yes it can.
The function org-set-font-lock-defaults sets font lock defaults for org mode buffers for all the types of org faces.
Not only the contents itself is important but also the order in which it is defined.
FYI, I will show pieces of code from the actual function (org version 8.3.4):
This block takes care of fontifing links. The type of link you are interested in is fourth line ('bracket).
;; Links
(if (memq 'tag lk) '(org-activate-tags (1 'org-tag prepend)))
(if (memq 'angle lk) '(org-activate-angle-links (0 'org-link t)))
(if (memq 'plain lk) '(org-activate-plain-links (0 'org-link t)))
(if (memq 'bracket lk) '(org-activate-bracket-links (0 'org-link t)))
(if (memq 'radio lk) '(org-activate-target-links (1 'org-link t)))
(if (memq 'date lk) '(org-activate-dates (0 'org-date t)))
(if (memq 'footnote lk) '(org-activate-footnote-links))

The comment lines (meta lines) are taken care by following piece of code:
;; Blocks and meta lines
'(org-fontify-meta-lines-and-blocks))))

The most easy (but maybe also a hacky) way to do it is remove the "bracket" s-expression from the list org-font-lock-extra-keywords and add it to the end of the list.
You can do so using a hook named org-font-lock-set-keywords-hook to "swap" these.
I am now using this code:
(defun vlk/org-font-links-in-comments ()
  ;; get bracket link s-expression for the font lock
  (let ((bracket-link-face (nth 12 org-font-lock-extra-keywords)))
    ;; remove the font lock from the list
    (delete bracket-link-face org-font-lock-extra-keywords)
    ;; add it to the end
    (add-to-list 'org-font-lock-extra-keywords bracket-link-face t)))

(org-add-hook 'org-font-lock-set-keywords-hook 'vlk/org-font-links-in-comments)

It certainly can be improved but it is functional for me so far.

