Since there are excellent VOIP programs for gamers (TeamSpeak, Ventrilo, etc.) I don't think your game would benefit from such a feature. The last time I saw a game where built in VOIP added some plus to the gameplay and fun was in Guns of Icarus Online.
But to answer your question: I don't know if it's possible with the vanilla C2, but it's certainly doable with a 3rd party plugin (you might just have to write it).
Edit: Here's an other topic about this: