Yes, if I understand what you're asking, it does indeed do that. It works basically like the pre-iOS7 Music app did. I love Audiotap. I do wish it would get an iOS 7 facelift, if nothing else to let us know that it is still being updated. But it works, and I have yet to find anything else in the App store that is better than Audiotap. One caveat: The machine I run Mediatap on is still running ML, but latest iTunes 11.1.2. So I can't confirm it runs fine with Mavericks, but I'd be surprised if it didn't.
I've been looking for an AudioGalaxy replacement for some time. Audiotap appears to fit my specific needs. Before purchasing this app I need to determine how browsing by "Genre" and "Artist" are handled as I have yet to find any videos or screenshots online that show the browsing structure used. Only interested in purchasing the app if browsing by "Genre" and "Artist" are handled just as they are with Apple's music app on iOS 6.13 per my iPhone 4, i.e. Genre\Artist\Album\Song, Artist\Album\Song where at the top of each level the option of browsing by "All Albums" or "All Songs" is also still offered respectively. Can anyone confirm on this? Thanks!