Yes, you can add custom connectors on Google Drawings shapes. The process isn't as straightforward as adding text or modifying colors and sizes, but it is possible.
To make a custom connector, you need three elements:
1) Select a shape - Start by finding the shape you want to add the connector to. You can make a shape from scratch by going to the "Insert" menu and selecting a shape. You can also use a pre-made shape from Google Drawings' collection.
2) Adding a connector - Once your shape is selected, you can add a connector by going to the "Format" menu and selecting "Connectors". Click "Add custom connector" and then choose the starting and ending points for your connection. You can also customize the appearance of the line in the Thickness, Color, and Dash menu.
3) Moving the connector - After you have added your custom connector, you can move it around the shape by dragging it with your mouse. This is a helpful feature when creating complex shapes with multiple connectors.
And that's it! With these steps, you can add custom connectors to your shapes in Google Drawings.