As above. I've translated a Word document containing a text box in CT. The text box content is in CT, but it is not exported when I export back to Word. (The original source text is still there.)
It looks like Word documents include the same contents of text boxes twice. One version is meant for modern MS Office (starting from 2011 or 2013) , and the other version called fallback can be opened in outdated versions MS Word. CafeTran imports for translation the newest version ignoring the old one. It can also be handled by LibreOffice 5. If the user saves the translated document in the new version of Word processors, it should also update the fallback section for old versions.