The problem is not so much whether the operation of ACF will work with WPML really, though I’ve not tried it. The main issue is that the WPML import is not adding the content correctly for ACF. If they are not supporting ACF fields than it’s unlikely that you’ll get this corrected.
I would suggest trying an import plugin that does support ACF, but I don’t remember if it supports WPML… I think it does. You could ask them. http://www.wpallimport.com/
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users