As long as Screen Sharing or remote management is enabled in system preferences, you can use the Screen Sharing app to connect to any headless Mac via any network connection.
Unless something has changed in 10.15, a MacMini does not initialize the GPU unless a display is attached. Which would include the h.265/h.264 quicksync tech in the Intel GPU that makes Sidecar and Airplay work. They make HDMI dongles specifically for fooling a mini that a display is attached so you would need one of those.
It would be awesome if Apple allowed you to initiate Sidecar from the iPad somehow. Assuming that isn't coming, I wonder if one could string together something via Siri Shortcuts, IFTTT and Automator/AppleScript to do the same thing? On demand Mac anywhere in my house? Yes please.