Does a unit gain the additional might from Assault if they move to an empty battlefield?

No, a unit does not gain the additional might from Assault if it moves to an empty battlefield.

According to Rule 733.1.c, Assault is functionally short for "While I am an attacker, I have +X [M]." Rule 733.1.d further clarifies that "Being an attacker means the Unit has gained the Attacker designation during Combat."

Because combat only occurs when units controlled by opposing players are present at the same battlefield, moving to an empty battlefield does not initiate combat and does not grant your unit the Attacker designation. Consequently, the Assault ability remains inactive, and the might bonus is not applied.