Is there any way I can attach a label to a face in a group?
I am drawing a piece of furniture and I want the label to stay on the face of a “board” regardless of which direction I orient the camera. That way when I want to make a nice printout my labels stay in place even if I move something.
Depends on what you mean by "stay on the face of a “board”. If you want it attached to the board but rotating to always face the camera (so it stays legible instead of foreshortening), you can use the text tool. Just keep the leader length to near zero. If you want the label to look like it is a real label pasted onto the board, make an image of the text, make a texture out of the image, and put that texture onto the desired face of the board.
Instead of using the Label tool, use 3D text. You don’t have to make the text 3D. Untick “Extruded”.