There are no studies at this time designed to determine whether or not having a good listener in your life will enhance cognitive function. It is possible a good listener may improve brain health by reducing stress and systemic inflammation, both of which can impair brain function over time.
Some studies have been limited by the fact that social-support was self-reported, therefore those answers may not be accurate. The researchers in those studies could not be objective in measuring social-support, and unable to assess the quality of the relationships.
One other limitation is that the cognitive tests, brain scans and social-support were all done at one single point in time. It may be possible that these ratings may change over time and that would alter the relationship of social-support and cognitive function. That means it can only be suggested that having a good listener and brain health are related, but not necessarily one causing the other.