I would say writing would help you be a better communicator verbally because as some mentioned here, the discipline and effort involved in writing helps develop your thought processes. Writing and verbal communication are forms of expression, means of getting your message across, so improvement in one should basically help improve the other.
However, as some have pointed out, public speaking is an entirely different matter. Speaking to large groups of people or in a public setting requires certain sets of skills. Writing will help, but not in all aspects when it comes to talking to groups of people or a large crowd. Otherwise, in terms of a casual conversation or a discussion among friends, family or people you are familiar and confortable with, writing is very likely to improve your ability to communicate your thoughts and feelings to them more effectively.