What role, if any, does visual aesthetics play in the design of modern airliners?
A friend of mine, who did the design of the Gulfstream G650 canopy, designed the cockpit windows on that jet after the lines of an Aston Martin sports car.  I suspect there are a few other features like that in various aircraft.

That being said, despite the aircraft design mantra of 'if it looks good it will fly good' most the the design choices made in aircraft is very utilitarian.  Aerospace engineers - and in particular the management at the major OEMs - are some of the most boring, unimaginative SOBs you will ever meet.  They generally leave creativity to the marketing departments and make every effort to pound flat any nail that sticks out.

The only exception to that rule that I can think of was Burt Rutan of Scaled Composites, who when his own way and designed unique planes as virtual works of art - but also were highly functional with great performance and capabilities.  From the Vari-EZ to Spaceship One, that guy is in a league of his own.