No. Hellhounds are standard enemy spawns in several Black Ops II Zombies maps (Mob of the Dead, Origins, Buried, Nuketown Zombies). They appear in Solo (Offline), Local Split-Screen, and Online modes identically.
Xbox Live Gold is required for:
If you play Solo or Local Split-Screen (no Gold needed on 360 for local), Hellhounds will spawn normally based on round progression and map mechanics.