Does a unit have assault if it's conquering an open Battlefield?

No, a unit does not have the Assault bonus when it moves into and conquers an open (unoccupied) battlefield.

According to Rule 807.1.c and Rule 807.1.d, Assault is functionally short for "+X Might while I am an attacker," and a unit only gains the "Attacker" designation during Combat.

As established by the RiftJudge FAQs (e.g., FAQ #863, #9076), moving into an unoccupied (open) battlefield initiates a non-combat showdown, not a combat. Because there is no opposing unit present to create combat, your unit does not receive the "Attacker" designation. Since it is not an attacker, the Assault ability remains inactive, and the might bonus is not applied.

Even if you successfully establish control of the battlefield and perform a Conquer at the end of the showdown, the Assault ability will not have been active during the move or the resulting showdown.