Data sources “connectors” for the desktop and service “connectors” for the cloud are two different things.
If you create a report in Power BI Desktop that connects to a PostgreSQL database data source, you can publish this report to PowerBI.com (the cloud) and configure the gateway to allow scheduled updates directly from the cloud (i.e., after setting up, you you can pull data from your PostgreSQL database through a gateway to a report in the cloud on a schedule). This seems to be what you wanted to do.
Additional information about the local gateway, including a list that shows that PostgreSQL can be used through the gateway for the scheduled update: https://powerbi.microsoft.com/en-us/documentation/powerbi-gateway-onprem/#list-of-available -data-source-types
However, you cannot create an empty report in the cloud and connect to the local PostgreSQL database. When you start with the cloud, you can only connect to a more limited set of cloud data sources (Azure and SSAS). In general, you almost always want to start creating a Power BI report in Power BI Desktop, and then publish it to the cloud.
Service connectors in Power BI are something completely different. They provide a quick way to connect to other cloud services that you can subscribe to and provide your personal data for reporting. For instance. if you use Salesforce, the Power BI connector connects directly to Salesforce for you. This is different than connecting directly to your own database. This is not your database that you are connecting to, but your data related to a third-party service already in the cloud. More information here: https://powerbi.microsoft.com/en-us/documentation/powerbi-content-packs-services/
Hope this helps clarify the situation.