Sure, if. But why should we assume we are far from a functional sequence? As this shows, we are actually much closer to folding protein sequences in non-coding DNA than you would naively suspect:
As we also know from studies such as the ones I cite in this post, simply obtaining a folding protein sequence means it is likely to have a useful biological function.
I’m sorry to have to tell you Bill, but this premise you can’t seem to let go of, that function is rare in sequence space, is just wrong. There is no support for it. Once you remove the strange and unrealistic requirement for a specific target sequence or target structure with a specific target function, but allow for any fitness improving function, functions are ubiquitous and unavoidable.