Will it increase the speed of your modem, no. Will your surfing experience improve, definitely. N and G have higher speeds at the same distance, and longer distances at the same speed. The response time will improve with the faster rate as well.
Personally I like to invest in network equipment, and would now buy a N router with a gigabit switch. They should start at $50 and go up from there with build quality and features. I wouldn't buy G models for sale currently as they are reaching the end of the technology and most models are built for economics, not quality.