Hi,
It's possible to animate leaves parameters to simulate small movement (as Rotation).
But we just noticed Ivy object is not properly updated on viewport and render sequences. We'll fix that.
On the other hand, to simulate growing, you can animate 'Growth Level' and 'BaseLine' parameters. But it may require some trial and error to get smooth results.
It also works better with high values of Growth->Segments (shorter branch segments), because it's not possible to animate the growth of each branch segment.