Sometimes, but not always.
There are many reasons why building age could theoretically impact energy consumption: changes to building codes, available technologies, architectural trends, and predominant business practices. Some changes over time may serve to lower building energy use, while others could actually contribute to higher energy consumption. For example, over time the average efficiency of boilers has increased, as has the efficiency of refrigerators in supermarkets; these trends are expected to lower energy intensity. On the flip side, glass buildings are more prevalent today and glass does not insulate as well as other building materials. Also, in some markets there is a trend towards more dense work environments, with open plan layouts that accommodate more workers. This increase in worker density could increase ventilation and cooling needs (conversely, a more densely populated office may require less energy for heating in the winter).
Given all of these diverse factors, there is not a straightforward relationship between building age and energy use. For some types of buildings there is no relationship whatsoever, for other building types newer buildings may appear to use more energy and for still other building types newer buildings may appear to use less energy. New York City, for example, examines age in their annual benchmarking report (http://www.nyc.gov/html/gbee/html/plan/ll84_scores.shtml). The 2014 report observes that for both multifamily and office buildings the median EUI falls within a similar range regardless of year built. There are a few decades that may peak outside of this range, but they tend to have lower sample sizes.
The bottom line is that you should not assume your building is or is not efficient because of its age. There are old buildings that are top performers and new buildings that are energy hogs. More important than your building age is how you operate and maintain your equipment.
You may want to see our related FAQ: Does the ENERGY STAR score account for building age?