Can an Arcane Firearm staff receive the d8 bonus when casting any of the blade cantrips?

Can an artillerist’s Arcane Firearm staff receive the d8 bonus when casting any of the blade cantrips? Since the staff can be both an arcane focus and can supposedly be used as a melee weapon.

Specifically Booming Blade and/or Greenflame Blade

Additionally, if yes, which damage does the d8 add to? The bludgeoning from the staff, or the secondary damage types?