I think one of the problems here is that people don't appreciate how much fashions, language and culture will have changed in 500 years. None of us actually KNOW the answer to the question we're discussing. But here's some thoughts (mostly reiterated):
(1) I don't think any actual Beatle music will be played (providing it survived). If a song or two is still around, it will be listened to by very few. Maybe some will play the songs and "record" them - as a minority pleasure. (But who knows what "record" will mean in 2505?) It'll be like those groups who play medieval tunes on original instruments. They are great, but what a minority!
(2) Every age has its "popular songs". But each age writes its own - it has no need for the love songs of yesterday. Tell me a hugely popular love song from the 1990s - easy; everyone knows many. But it gets harder as you go back. 1940s? 1920s? 1880s? Do you see what I mean. That's why Yesterday, Let It Be and their ilk will not survive.
(3) The Beatles will be mentioned and written about in any history of post-WW2 western culture. As part of this, their ground-breaking creativity is going to be of interest. My view is Lennon is the original mind in the group. Out of that mind came Walrus, SFF etc. That's where they rose above their peers musically. No other group has the equivalent of Walrus and SFF, but plenty have their Yesterdays. So if anyone's interested in the group 500 years down the track, it's not going to be what so many can do (Yesterday, Let It Be) - it's going to be what they did that NO-ONE else could do!
In other words, in 500 years it won't be a popularity thing.