I thought about that, but I actually liked the sort of natural grain pretty well. In my case, only the top is finished solid. The back and sides are finished natural. But that's just me. It could work if you wanted to have the back be a solid color. But I think it would be a lot harder. You would need to drill all the way to the top without going through, and then you'd have to figure out how to to get the plug to match the curve of the top. Going in from the top you only have to get the plug a little deeper than the post.
Again, in my case, the veneer was doomed anyway. These are really cool kits, but my two main beefs with them are that the veneer is too thin, and the center block is too narrow. 12mm more on the center block would make it much stronger laterally, and allow more bridge choices. And I would MUCH prefer to have the back veneer on both the front and back (like the old Gibsons actually had) rather than the flame maple tops that get damaged if you breath on them too hard.