Not really, the balloon gains volume at the same rate as it gains mass, so its buoyancy doesn’t change. Or at least it wouldn’t, if it weren’t for a a small detail: the air inside the balloon gets compressed, which makes it heavier for its size, making it gain more mass than it gains buoyant force. That means the scale would read an increase in mass, representing the extra amount of air that shouldn’t be occupying that space, were it not compressed.