I don't think so. The Americans have had these budget disputes for what seems like forever, and the public just rolls their eyes each time, they've got so used to it.
In 2013, the govt was shut down for two weeks, and the country still managed to function (because the states and cities run so much of it).
Its happened before, and this shut down was anticipated. Any effect on Bitcoin would already have been priced in before it happened. Bitcoin's price recovery is nothing to do with the shut down.