As per my knowledge,
you cannot use a single connection for multiple shared mailboxes in triggers. Each shared mailbox requires its own Outlook Application Scope or Exchange Connection. This means you will need to create a separate connection for each shared mailbox you want to use with a trigger.
For each mail box rather it be a shared or dedicated mailbox you need a separate connection to access it..so yes for every connection you need a separate one..
but if you want to setup trigger for one mailbox then you can setup multiple as well ..