When I read The Time Traveller's Wife by Audrey Niffenegger, Henry's lecture to the "baby punks" put me in the mood to go and listen to some of the bands he mentioned. His repeated appearances at the Violent Femmes concert also made me go an put on Blister in the Sun.
Emergent Publishing's Literary Mix Tapes anthologies usually make me want to listen to the songs that inspire the stories, though I confess that taking part in the anthology From Stage Door Shadows put me off Elton John's song Tiny Dancer because I had listened to so many versions of it while struggling to write my story.
A BIG YES.. I try out several things that I've read in novels. One of the best examples is searching everywhere for a book a character was reading.. others being trying to find if the hidden treasure can be found in a certain spot, if a song or music, a character listens to, does exist etc.
It depends on the book, and what context the music is mentioned in. If it's an integral part of the book or a character's life, then I get curious enough to listen to it. If it's just a throwaway line or two, there's less chance I will.
I read (audiobook) a trilogy by Robert J Sawyer (Wake, Watch , Wonder) where the main character always talked about her favorite band. I have googled every possible spelling of the name of the band but it doesn't exist! So frustrating.