The Everdrive 64 doesn't add any new audio hardware to the N64, so any new music or audio tracks would still have to be played by the N64 itself, meaning that it couldn't be better quality than the N64 could produce (though the N64 can produce excellent sound and music, properly programmed). A skilled hacker could certainly add more or longer music to any N64 game, storing the required data either by extending the size of the game rom to the maximum N64 size, or by directly reading the data from the SD card via data files that are separate from the game rom file itself.
The latter solution would be the best in most cases, as the maximum size an N64 game rom can be seems to be only 64MB, and certainly the Everdrive 64 (any ED64 revision) doesn't come with enough RAM to contain any significantly larger game rom than 64MB.
So yes, it's perfectly possible to have the N64's Tony Hawk's games have the same full soundtrack as the PSX version, but whether or not someone with sufficient programming skills will take the time and effort to do this doesn't seem too likely. The N64 is notoriously difficult to program anyway, and few people seem to bother programming the N64 (given how popular the N64 was and is, it does seem surprising that it's current hacking/programming scene seems so sparse), and since N64 hacking is spread out over the internet, instead of being largely collected on either one site or a few connected websites, then even if someone does convert the N64 games' audio to the PSX versions' soundtracks, then we here might not get to hear about.
