Agreed that trying to evenly light an area that large especially if it’s just a cover will be challenging (not impossible, but challenging!)
If the main housing is opaque, that type of light pipe would just give you some soft illumination on the top surface at best.
My suggestion would be to design a more local lightpipe area that would still meet your need, and creating that outside housing as 2 pieces or a two shot part (opaque over clear). As mentioned, creating a smooth uniform glow with limited LED space, a small number of LED’s and light across surfaces in 5+ directions is very challenging. Especially if your internal housing remains black, since that prevents the light from bleeding out to the housing.
From the scale of your exploded diagram it looks like you have less than 1cm for your LED’s to illuminate, which means the spread of those LED’s will only form a lit area that is very narrow. Typical tricks would be to try to move it as far away as possible, and pipe it towards the top, but the board means half your LED cone would be cut off by the PCB itself.
You may be better off shooting those LED’s to the sides, and illuminating the edge of the product. 4 LED’s (two on upper and two on lower area of PCB) would give you a better distribution along the side, and you may be able to design some pipe features into the outer housing itself to better disperse the light.