Nope.
The Dragon was cast down to earth after Christ ascended to Heaven.
The reason?
The Devil/Serpent (Dragon) had been the accuser of the Saints before the throne of God in Heaven.
Since Christ remitted their sins on the cross,
and resurrected to prove their justification He purchased with His own blood,
there was no more of which the Devil could accuse the Saints.
He was therefore cast out.
The Dragon since then has been making war against the Saints only on earth,
as we can see on a daily basis.