No, if payers wore mic's you would hear it is very verbal as well, just lip read sometimes or in preseason watch a warmup game since the crowd is small you can hear all the calls, "wazza backdoor" etc, is mainly between one to three words, but you use everything you have. Then half-time, the strategy sessions are all talk. I forgot to mention when the coach can't speak english or any other home lanhuage but still is successful.
Southampton are currently managed by a guy who speaks no English: http://en.wikipedia.org/wiki/Mauricio_Pochettino
Giovanni Trapattoni manages the Republic of Ireland national team (and is one of the highest paid international managers around) speaks notoriously poor english. When he managed previously in Germany, he was also known for mangling the local tongue.
Jose Mourinho is a fascinating character. He is highly educated and speaks 5 or 6 languages fluently. He is one of the most tactically astute managers in the modern game. He's also notoriously paranoid, convinced everything is a conspiracy against him, which seems to stem from an incident in his childhood where an uncle was a wealthy member of the ruling elite, but a peaceful coup meant that the family lost a lot of their wealth. Here's a good documentary covering his recent managerial career: