Yes! It plays a major role. Communication skills are very much required to put forward your views and actively participate in a discussion, especially brainstorming sessions.
I would like to answer this in the context of non-English speakers to show its importance.
Communication for these guys is split into two parts. All the vocal and visual expressions one side and their English on the other.
Even though they are smart and voluble, when it comes to conversing in English, they surely have hiccups. Most of the times, they face hard times to put forward their point to fellow english speaking programmers as well as to actively participate in any discussion. Many people dont even utter a word because of the fear of sounding awkward.
So, ability to converse in the language plays a major role when there are people from diversified backgrounds.