Playing with DarkholmeTenk's Tardis mod and suggested having his magic doors render what's on the other side, but he said it wasn't possible with the looking glass API:

darkdurza commented an hour ago
I think it would be awesome if, instead of the star background, the magic doors had an image of the room on the other side.

DarkholmeTenk commented an hour ago
Nope, tried this, couldn't get it to come anywhere close to working. Too many chances for door a -> door b -> door a rendering causing an infinite render loop, when I tried with looking glass and I don't have the skill nor time to implement this myself.

Is there no way to have it not render any looking glass views, or only render up to X views deep?

In theory, I don't see any problem, since currently it renders a view to texture, so it would render a texture inside a texture. I have not tested this though

Since LookingGlass just does a render-to-texture, there should be no loops. However, using that for portals results in some very flat looking portals. I've been working on some proper portal renders, but I think that will get backburnered to after updating and other fixes.

To answer the question, you should see the render as it was last frame.