When playing Ambush as a Reaction into a BF with my Defending Unit, does the Ambush gain Assault if it contains the Keyword?

To answer your question: No, a unit played via Ambush into a battlefield where you already control a Defending unit will not gain the benefits of Assault.

Reasoning

1. Assault Requirement: According to Rule 807.1.c, the Assault keyword is functionally short for "While I am an attacker, I have +X [M]." Rule 807.1.d clarifies that a unit only gains the "Attacker" designation during Combat.
2. Designation Conflict: When you play a unit via Ambush into a battlefield where you already have a unit designated as a Defender, you are joining an ongoing combat as the defending player. Because you are the defender, your units at that location hold the Defender designation, not the Attacker designation.
3. Passive Ability Status: Since Assault is a passive ability that is only "on" when a unit is an Attacker (as per Rule 807.1.d.1), and your unit is entering the battlefield as a Defender, the condition for the Assault bonus is not met.

Summary of Interaction

• Ambush: Allows you to play the unit as a [Reaction] to a battlefield where you already control units (Rule 822.1.b).
• Assault: Remains inactive because the unit does not gain the Attacker designation in this scenario.
• Defender Designation: Any unit you control at a battlefield where you are the defender gains the Defender designation. If your unit has the Shield keyword, it would benefit from that instead, as Shield is active while a unit is a Defender (Rule 814.1.c).

This interpretation is based on the definitions of the Assault and Defender keywords provided in the core rules. No official FAQ exists for this specific interaction, but it follows directly from the requirement that Assault only functions while a unit is designated as an Attacker.