Having text be a child to a game object?

Depends on the Canvas Render Mode type. If you make the canvas Screen Space - Overlay, then all elements of that canvas will essentially be drawn to the screen. If you use Screen Space - Camera, then it's drawn to the screen of only that specific camera (useful for using different cameras for different 'layers' of UI drawn on top of eachother), and if you use Screen Space - World, then it's drawn in the scene the same way any sprite object would be, and can be behind other non-UI sprites and 3D models, etc....

Use a TextMesh instead of a Text component. Put the TextMesh on a GameObject in the scene where it should be, but don't use the Canvas (which is generated automatically when adding Text components).

Explanation: Text components are used for User Interface on the Canvas. The Canvas is just "held in front of the camera" like a head-up-display. TextMesh on the other hand is an actual "in game object" and stays whereever you put it in the world (as long as it is not a child of the Canvas which is as stated above "moved" with the camera.