Does the exchange connector need to be installed on all Mailbox server? If not, is installation on multiple Mailbox servers supported in order to drive HA?
As far as I know you setup one Exchange server for the Nintex environment to use. The Exchange Connector for SharePoint should be created on this Exchange server.
If you review the Exchange connector install guide found here:
It specifies the following:
If your Exchange environment is implemented across multiple machines, the Exchange Connector Service should be installed on the machine running the Exchange Mailbox role.