To simply put it, yes. Pikachus cry will change to it saying its name even if you transfer it from pervious gens, because it's original cry isn't in the game's data.
They made it have that changed cry, because it is the mascot of the franchise, and thus, it gets special treatment, such as exclusive held items (the light ball), exclusive moves (Volt Tackle), cosplay Pikachu, and its unique cry of it saying it's name.
Source: knowledge
