It has for me, I have taken a liking to the Ink Spots song from Fallout 3 and I like Blue Moon. If I hadn't of played Fallout, I don't think I would have ever liked this kind of music.
Yes, it totally has. I actually just got done listening to a bunch of Bob Crosby :tops: . Mad props to Fallout 3 for bringing such classy music to the radio stations. Didn't feel quite the same with New Vegas, but I'm not hugely into the country 'twang' and there didn't seem to be enough Sinatra/Martin.
Some of my other favourite artists that people should check out (many from the F3 soundtrack):
Louis Jordan
Ink Spots
Ella Fitzgerald
Louis Armstrong
Billie Holiday
Eileen Barton
Wayne Newton (some of his earlier 1960s stuff)
Would also recommend looking for the Mafia 2 soundtrack, it has a lot of Fallout 3 type music that might pique your interest in different bands.
Come on now, how could anyone not think songs like this are awesome?:
http://www.youtube.com/watch?v=YdQJ3Q0uhYE
http://www.youtube.com/watch?v=LmtL8S87UZ4