Sure it can be done and if you tell the material to “uses morph” the UV mapping should not be a problem but you should be able to set up different UV mapping channels.
You can set the character up to use a full body morph but since UE4 does not support progressive morphing you will have to set it up using a series of progressive targets to avoid the pop from point A to point B effect. Since morphing is additive the rigging should not be to much of a problem with a little planning.