Is there any way to import character into Unity which has morph applied to it?
It doesn't look like it. See Blend Shape Animation?. Plus, from the Unity Manual page: "Unity does not import blend shapes. Use Bone-based animations instead." From HowTo Import from Maya.
Update: just found a similar question (okay, identical question) at: Unity supports Blendshape?. The important part of that, is they list a site where you can vote on upcoming features, such as Built-in Morph Support. So go vote, if you want that feature.
Technically there is a way (i.e., program it yourself), but there are no built-in functions to do this, no.
MegaFiers will deal with the Vertex animation as well as morphing and all sorts of deformations. It has an exporter for Max and blender, you can find more info on the forums http://forum.unity3d.com/threads/89750-Mega-Fiers.-A-mesh-deformation-system-RELEASE