How to show the number of times a page has been shared by all services total? Is it possible to show a small block (using code or a module or something) that shows how many times the page a user is on has been shared using ANY of the available sharing methods?

For example, I'm trying to use the social sharing module AddThis and I'm showing the Facebook, Twitter, and Pinterest, and Email icons (although I also want to use the 'more' icon to show all the others).

And I want a little box to the right of those that just shows how many times the page has been shared. Is this even possible?
you could use:
Social Share Counter Module

This module is clearly inspired by the share buttons used by Mashable.
This module gives the share counts for only Facebook,Twitter and more
which has some excellent features in more elegant manner. If you have
a website, then you definitely need this module.

If you still want to use AddThis, then use Social Stats Module

This is a statistics module. It provides data from various social
media sites. The data which is saved per node. It includes data from:
Facebook : likes count, shares count, comments count &amp; total count.
Twitter : tweets count.
LinkedIn : share count.
Google Plus : plus one
count, share count &amp; total count Total Share Count : total across all
available social networks Note: This module is intended to collect the
statistics per node from the networks mentioned above.
It does not actually provide sharing widgets for the social networking
sites. They have to added manually, or using other modules. List of
the modules recommended to use alongwith Social Stats are:

Service links
AddThis