I believe it can. It might take a federal warrant or two to do it, but every single dollar that they shell out it can in fact be traced.
All you need is someone in the Department of Justice with the intestinal fortitude to follow through.
Put it this way, nearly every dollar transits a bank these days, some way or another. And you can get a detailed running of an account online at most banks. So it’d be a fairly trivial matter to trace the so called ‘dark’ money. You just need the manpower to do it.