This article describes the process to determine what hosts are connected to a given datastore, including their status (for example mounted but not actively connected).
vSphere (all versions)
This information can be seen by navigating to the datastore in question in the vCenter UI, then selecting Configure and then "Connectivity and Multipathing".
From this page, all hosts connected to the datastore can be seen as well as their connectivity status to the datastore in question: