Listing rudimentary language proficiency in an application in that country despite English being working language
I think yes, you should list it with caveats at the end of CV, using something like


  Languages:
  
  English (fluent), Arabic (basic passive)


and it the country in question is in Europe, just use the EU proficiency levels: for example,


  English (C2), Portugese (A1) 


Frankly, I don't think it would help. It can't hurt and it maybe gives you some points for being keen, but the time you waste thinking on this might be better spent studying something. Maybe even the language in question.