Doubt it. How do you imagine music will be like in 50 years? I doubt you would expect it to be the same as it is today, right? You might not know what it will sound like, but I suspect you would think of it as something that's definitely going to be different to what we listen to today.
So the setting being 50's vision of the future should have things that are different to what said 50's actually had, because everyone expects future to be different to the present.
So music in fallout sounding like it's from the 50's is completely illogical.
That's not really a valid comparison because the real world wasn't undergone such a complete and total cultural regression in the modern day like the Fallout world did. Music in the real world keep changing because culture keep changing into something new. The Fallout unvierse just went into a big loop sometime after the counter culture era of the 60's, and before the 2240s/50s.
Similarly, idealized versions of the future always include things like music from whatever time period is making up their version of the future. Humans are, by nature, short sighted, and prone to simply jamming in whatever is around them into the spaces. Many old movies and the like from the 50's, showing idealized versions of the future, included music from the 50's in their idealized versions of the future becuase
A. That's the music they had on hand
B. Since it was their own era's music, they naturally had a superiority complex in regards to it, and thus thought that any sort of perfect future would have it too because its just "that good" in their opinion.