Not really. We can see how much bitcoin donations charities received, but we have no way of knowing how they were spent. We probably can't trace the coins back to the anonymous donator either.
Usually charities are already quite open with the donations they receive and what goes where. I think they even have to be by law in a lot of countries to clamp down on wrongdoing.
It provides anonymity in that you don't know the person who sent it. If I donate with my creditcard that info will forever be stored somewhere and my real name and identity will be exposed (possibly even publicly in some scenarios). If the money just comes from 14TiiZRzqYv9t14jQ8UBhbCmmeDed6GPyh then the most someone could find was that it came from MUFC but I could send money from an address not tied to me if I wanted further anonymity.