wow, I learned a whole lot from your answer Nicholas, but still not quite enough to make this work for me.  After some puzzling over the syntax for character values, I believe that what I want should be something like this:

(add-function :before-until electric-pair-inhibit-predicate
              (lambda (c)
                (and (eq ?\[ c)
                     (eq major-mode 'org-mode)
                     (memq (char-before (1- (point))) '(?\[ ?\])))))

The manual says to use advice-add instead of add-function for these cases, so this could be written like this instead:

(defun mwp-org-mode-electric-inhibit (c)
  (and
   (eq ?\[ c)
   (eq major-mode 'org-mode)
   (memq (char-before (1- (point))) '(?\[ ?\]) )))

(advice-add electric-pair-inhibit-predicate :before-until #'mwp-org-mode-electric-inhibit)

it seems to sort of work.  That is, the code is effective, but it doesn't do what I want, so I had to think about the desired behaviour, which is maybe too complex for this modification:

when I start a link [
go ahead and add pair to
[]
when I add a second [, don't complete
[[]
this is what my code does!

but what I really want is, when I finish adding a link reference, somehow allow me to stay inside the link to add the link text:
[[https://google.com]] --> [[https://google.com][]]
with point between the final [ and ]. 
This seems like it needs a more complex intervention. 

For now I've just turned off pairing of brackets entirely:

(defun mwp-org-mode-electric-inhibit (c)
  (and
   (eq ?\[ c)
   (eq major-mode 'org-mode))

This works fine, though I'd still like the other :-/ 

Thanks Nicholas!
On Sun, Oct 21, 2018 at 3:28 AM Nicolas Goaziou <mail@nicolasgoaziou.fr> wrote:
Hello,

Matt Price <moptop99@gmail.com> writes:

> - electric-pair and autopair complete [[ immediately, and don't seem to
> allow me to skip past the closing brackets, so if I try to type [[
> https://link.to.somewhere][link text]] I end up with
> [[link.to.somewhere]][link-text] .

I use C-c C-l to insert links with description. However, electric
pairing does get in the way when writing sub/superscript. I use the
following snippet to work around the issue:

   (add-function :before-until electric-pair-inhibit-predicate
                 (lambda (c)
                   (and (eq ?\{ c)
                        (eq major-mode 'org-mode)
                        (memq (char-before (1- (point))) '(?_ ?^)))))

I guess you could do something similar to disable pairing when entering
a bracket link.

Regards,

--
Nicolas Goaziou