Do I Need to Have a Workflow?
Yes, you must have at least one Workflow setup in order for anything to sync across your systems. Workflows are like the door that allows your data to come through.
If you don't care about restricting what types of records sync, you can simply leave the Default Workflow in place when you first visit the Workflow page. The rule in this Workflow allows for any record type within any of the Connectors you have setup to sync from one system to another.
If you want to restrict records from your Connectors, then you'll want to add Custom Workflows.
If you don't want any new records to sync from one system to another, then simply exclude this Connector from any of your Workflow rules.