There are two separate behaviors expected when using Opportunity Partners in Conga Grid.
In Salesforce Classic, users have the ability view Partner records and create Partners in a new window by clicking the new record button. Due to Salesforce restrictions on the object, no inline capabilities are supported.
In Salesforce Lightning, users have the ability to view Partner records, but cannot add them in a new window or inline. These options are disabled because the object is not currently supported in Salesforce Lighting.