No, if an intelligent civilization were on a planet traveling at close to the speed of light, their perception of the age of the universe would not necessarily remain the same. This is due to a phenomenon known as time dilation, predicted by Einstein's theory of relativity.
According to special relativity, as an object's velocity approaches the speed of light, time appears to pass more slowly for that object relative to a stationary observer. This means that for the traveling civilization, their perception of time would be different compared to an observer at rest.
If this civilization were traveling close to the speed of light, they would experience time dilation, and as a result, their clocks would appear to run slower relative to an observer who is not moving at such high speeds. This effect becomes more pronounced the closer the civilization approaches the speed of light.
As a consequence of time dilation, if the civilization were traveling near the speed of light for a certain period, they would perceive less time passing compared to a stationary observer. Therefore, their perception of the age of the universe would be different from the 13.7 billion years typically estimated by Earth-based observers.
It's important to note that the effects of time dilation become significant at speeds approaching the speed of light, and in practical terms, achieving such velocities is currently beyond our technological capabilities. However, this explanation provides an understanding of how time dilation would affect the perception of time for an observer traveling at relativistic speeds.