Cross Cultural Communication skill apply not only to ELL learners but to English speakers also. In teaching adults from different cultures, the instructor must be able to adapt to deal with those differences. Pre-testing can help alleviate language barrier and some knowledge based issues, but it would be well worth the time to invest in cross cultural communications training for the instructor.
It also applies to teaching adults from different professional background... i.e. each profession has its own culture and specific language. (police, nurses, military, engineers, teachers....)