Is it possible to display GUI elements as part of the world? For example a panel on the wall the player can interact with.
As stated in the comments below your question you should not attempt to render anything from the GUI-class as a part of the world.
If you want the panel to look like a real screen with certain effects on it:
Setup the panel with the interaction elements as colliders. The colliders will be there to interpret interaction events. Have a look at OnMouseOver(), OnMouseDown(), OnMouseUp() but perhaps most importantly OnMouseUpAsButton().
Render the panel to a Render Texture with its own camera. Setup the graphics for the panel, this could be a static background and the buttons as 3d-meshes (preferably sprites). Use layers to only include the objects needed. Connect the colliders on the 3d panel to the rendered objects to make them interact. Here you'll probably want a texture sheet and offset of the texture when interacted. Set the rendered texture as a material of the panels screen to make the screen output what the panel's camera sees.
On the rendered camera you can have all sorts of post process effects to make this look like a real screen. Also keep in mind to check distances to the panel and if the player is actually looking at the screen, if the player is not then disable the camera for the panel.