Yes it can be done, but is pretty difficult when it comes to the door panels and durability is not a strong suit.
Basically you re-wrap the dash panels with a cloth cover of your choice, using spray contact cement- the truly professional variety from a woodworking supply store is recommended for any chance at durability. Epoxy would be good for permanent adhesion at some locations as well. The door panels are the most difficult as the insert area is difficult to handle, and the curving back edge generally requires a seam unless you have stretchy fabric, which is harder to glue down.
Here's some shots of my old NA, unfortunately I don't have any from when I did the entire front area with the black, and had to replace the ds door panel vinyl.
This work lasted about two years before some areas began peeling due to sitting and heat/weather effects (cold/wet, hot/dry) and I had to do this job twice as the first fabric I used was too thin/wrong color when stretched. I was unable to find a correct color match for the vinyl, and used a piping rod style of piece to fit into the recessed area between the cloth and vinyl, and also made arm rests as you can see.

Arm rest core

And finished, bolts are to fasten.

A professional upholstery shop would probably do better for durability with leather as is in my TT, but at a higher cost of course.
My TT interior with leather inserts, and I also made it arm rests.

As you can see the shop that did this work did not use piping, and the leather has stayed down well to this day almost three years after I purchased the car.
Good Luck!