According to the Centers for Disease Control, the answer is yes. The vaccine will give you full coverage for the entire flu season. In fact, the CDC recommends that people get their shots as soon as possible, because the flu virus can't read a calendar, and this year, there could be early outbreaks, so why not be protected?
The CDC suggests that everyone six months of age and older get a yearly vaccine. As of now, there is very little seasonal flu going around, but health experts say, you can never tell when the flu will hit. Better to be prepared.