Only at the steepest levels, according to Tim De Chant:
[Vehicle miles traveled or VMT] only really declines substantially at the highest housing density — over 5,000 units per square mile, or about the same as Chicago. To halve the VMT of the highest mileage households, you would need to increase housing density in those areas 20 to 100 times.
A better short term solution is fuel efficiency:
One of the main arguments behind higher density living is that it will reduce our carbon footprint. While density may be a better long-term solution, right now the most expeditious approach is to increase fuel economy. Rebuilding neighborhoods will take decades. In that time, most people will buy at least a handful of new cars, primarily for commuting to work.
The Dish 