If I understand your question correctly, Greenskinz are still part of the Destruction Grand Alliance, and gain access to Destruction Battle Traits, Command Traits and Artefacts*. However, your army loses the "Greenskinz" allegiance if you select units that aren't listed under that. So if you add a unit of Orruk Ironjawz Brutes (Ironjawz alligence), the Boar Boyz stop being a Battleline unit.
*Unaware of the Greenskinz got Battle Traits, Command Traits and Artefacts in the Destruction Alliance book, but I don't think so, so regardless you'll always be selecting Destruction allegiance stuff from the General's Handbook.
As an comparable example, a Stormcast Eternal army, made up exclusively of their units, would let the player choose to either roll on the ORDER Battle Traits, Command Traits and Artefacts, or STORMCAST ETERNAL charts, because it's made up exclusively of units with that keyword. If however, the player were to add in FREE PEOPLES units to represent a mixed force, he can only roll on the ORDER charts.