I have not had tried an actual sync solution between WP and Magento, but there are some plugins and solutions by which will allow you to run a WP site over magento sessions.
Mage Enabler. This is a WP plugin that gives raw access to the Mage object - you can use it like single login and even access Magento methods within WordPress (pull templates from Magento, display categories, products and checkout from your blog etc etc and much more).
There is also a Fishpig plugin for this purpose. See http://fishpig.co.uk/magento/wordpress-integration/customer-synchronisation/
While I have not used this plugin on any project yet.
Other solutions to consider below...
Or you can ever build a bespoke solution
Just check, if a customer session is returned through mage, and check for WP sessions also. If WP session is not set then the user is not logged in. Create the WP user with a common password and inject the login. You can start this from here.