I don't see where they get the description as a "white solid". When I read "white solid" I'm thinking "MarineTex" or similar products, but they appear to have actual white pigments mixed in. That's not the case for GelMagic.
It's very slightly amber in my recollection (pale honey) and opaque in a milky kind of way. Definitely still translucent. But I doubt that it would show very visibly if you had a narrow glue joint viewed edge-on, and not at all in cases, for example, where you had a bit of overspill around the glue joint that you wiped off (leaving a very thin layer).
To make any gaping joint blend in more, you'd might experiment with mixing the epoxy (whichever you end up using as glue) with a bit of sawdust (sanding dust) from the same wood. In any case, if you are going to work to exacting standards, you are best off making a small test piece to verify that you got the process down.
To give you an idea, I found a messy sample I had lying around and took a picture. In the top half, you can see a raised ridge, that one does look very strongly milky as the light hits it. In the bottom half (you may have to scroll) you can see a gaping joint, part of it is filled, and part of it is only partially filled. The effect in one case a bit like tapioca, in the other you can see a bit of the amber coloring surviving. (Image is magnified at least 200%).
Over the entire surface there's a thin, but still substantial film of GelMagic of varying thickness, and you can see it's hard to impossible to tell it's there in the picture. It's just not opaque enough to show up in very thin to medium thin layers -- once you add some layer of ClearCoat and whatever varnish you are using, I predict any accidental thin layer of GelMagic will be invisible.

- GelMagic on soft wood. Magnified. For scale note the wood grain.
- DSC08302-crop_1024.jpg (92.54 KiB) Viewed 20137 times