Yes, I think you should be able to do something like this - with enough effort and time though 
Lets brake this down into different parts:
- You need to be able to change parts of your character, e.g. the hair, with different skeletal meshes. UE4 can do this, no problem.
- Same goes for different textures, no problem.
- To be able to deform the character shape you can use Morph Targets included in the fbx pipeline
- For posing you have to use some kind of FK/IK system
So in conclusion I say you can achieve something like that with UE4