First of all you can use blendshapes for anything you think it might be usefull for i.e deformation of clothing but I don't think blend shapes would work very well for tree growth since you don't really have any control over when and where things like branches will appear.
Another possibility would be paint effects since you can animate the tubes but again not as easy as it sounds and would take a lot of tweaking,heres some info I found on High end

https://www.highend3d.com/maya/faqs/p...ation-228.html

Somthing elese to consider would be maybe to animate your extrusions of the branches using an animated sweep perhaps.