According to Bulbapedia
Likewise, if a Pokémon normally immune to Ground-type attacks is made vulnerable, they will be affected; if the Pokémon is under the effect of Gravity, Smack Down, a move that negates Levitate (such as Gastro Acid or Simple Beam), type change effects that remove Flying-type (such as Soak, Conversion, Camouflage, or Color Change), or a held Iron Ball, it will be unable to escape.
So theoretically your situation comes under this subject.
Though when we took it to battle this is what happened.
The foe's Dugtrio used Pursuit!
Jirachi lost 16% of its health!
Jirachi's Air Balloon popped!
Jirachi, come back!
Now this may have happened because maybe Showdown is not yet programmed for this situation.
Credit to Derpalot and Flare
So as of yet I do not know the true answer, this is why I am going to try and take this up with some researchers at Smogon who can find the final answer.