Uptown-
Yes, the panel is covered in headliner material. A couple places that could give problems are the metal grommets around the wiper on-off switch and wiper speed control. An easy way I found to handle the grommet problem was to visit a local craft shop and pick up a grommet set (washers and press stud). Unfortunately, you end-up buying a lifetime supply of the metal grommets but they are not particularly expensive.
The second potential is covering the radio head (only '35 Ford). It is hard to attach the cover to the metal housing without creating wrinkles It can be done but it also can be frustrating. I have seen some radio covers covered with a thin layer of foam rubber to the metal housing. Then the cloth is then applied over the foam rubber. This does lessen the wrinkle problem and looks kind of neat but diffidently is not original.
Hope this helps.
Tom