Tamir Lousky shares an Addon for Blender that will allow you to animate the growth of Ivy or any branching object. The Ivy Growth Generator for Blender animates growth of ivy and trees that have been created by the Ivy Generator and Sapling Addons.
This add on animates the growth of ivy and trees created by the ivy generator and sapling add ons
The Ivy Growth Animator uses the Build Modifier and Shape Keys in Blender and can actually animate other objects in blender, however Tamir notes that it will only work with “branches” that are created from a single curve object.
There is also a caveat for animating the leaves in that it requires all the leaves to be represented by a single mesh object with each leaf being a separate loose face. Check out the Ivy Growth Addon for blender here, and also the Ivy Growth Animator can be downloaded here.