Can RawTherapee preview only the cropped area full-screen before export?

I just discovered a way to do this. I'm using RawTherapee 4.2, but from your screenshot, I think this feature is in the version you used, too. It's in the toolbar just to the top right of the image. From my system:

The blue, green, red, and gray squares let you preview individual color or luminosity channels — they're toggles you can click on. To the left of that, there are three horizontal bars. The tooltop is "Background color of the preview", and they are, in order from top top bottom, Theme-based, Black, and White.

When set to Theme Based, I get the behavior shown in your preview: the cropped-out area is darkened but still visible. If I, instead, change to either black or white (default keyboard shortcut seems to be 9, by the way), only the selected ("cropped in", if you will) part is shown.

This doesn't automatically make it full screen, and the zoom buttons at the bottom still zoom to the original border, but you can use the + / - magnifying buttons to get it approximately right without too much hassle.

(Darktable, as matt.nguyen mentions, behaves differently — the cropped-away portion is only shown while the crop tool itself is highlighted. That kind of modal behavior is common in the Darktable UI, but Rawtherapee doesn't generally have a corresponding concept of "active module".)