If we install a new workstation without Auditor, will the Auditor tables we are currently monitoring through Auditor continue to be tracked?
This depends upon what type of audits you have defined. For SQL Table audits, individual users do not need Auditor installed on their machines in order for these audits to take effect, so yes, these would continue to be tracked. However, in the case of Form audits and Table audits, everyone whose actions you want to be audited needs to have Auditor installed on their workstation.
Note: The person who administers the Audits will need Auditor installed regardless of the type of audits you have defined.