So you want a translucent case which can hide the LEDs when they are off, but show then when they are on? I agree this might not be the best fabrication method for this effect. I would print a case with a window and use a tinted laser cut plexi glass. That said, it wouldn't be that hard.
There are a few catches. First you will have 3d printing texture. The lines and ribs. So there will be light distortion. However it can be minimized by either using a resin 3d printer with ultra high quality, or by having the window side printed on the bed, avoiding the ribbing. Albeit it is still not perfect.
I would look at translucent materials such as Tglass. Using these clear materials you can either ally a window tinting yourself or find a seller that has a very dark, yet still clear material. This will allow the effect where a LED is off and you cannot see it, and when it is on - see it.
Tglass can be treated to be extra clear. Looks like they treat their material with XTC-3D for very translucent effects.
There are other options such as Resins, clear ABS, and PolyCarb (high temp)
All that said. Laser cutting is really what you want.