If someone moves a unit to a battlefield to start a showdown, can they still move the VI with ganking to that same battlefield before passing priority?

No, you cannot move a unit with Ganking to a battlefield after a showdown has already been triggered at that location.

According to Rule 143.1.c, a Standard Move (which includes Ganking, as per Rule 143.4.c) cannot be performed during a Showdown. Once the initial move has occurred and the Showdown has been triggered, the battlefield is in a state where standard movement is restricted.

However, you can move multiple units simultaneously to the same destination as part of a single move action, provided they are all eligible to move there. If you want to move both a unit from your base and a unit with Ganking from another battlefield to the same destination, you must declare them as part of the same simultaneous move action before the Showdown begins.

Summary of the sequence:

1. Declare: You declare all units moving to the same destination simultaneously.
2. Move: The units move from their respective origins (base and/or other battlefields) to the destination.
3. Exhaust: You exhaust each of the moving units.
4. Showdown: The Showdown triggers only after the simultaneous movement is complete.

Once the Showdown has started, you can no longer use the Standard Move action to bring additional units into that battlefield.