iExplorer is the perfect app for transferring music from an iPhone, iPod, or iPad to your Mac or Windows PC and doesn't have the restrictions that iTunes has when it comes to importing music, but the Media Library section is read-only which means you won't be able to add any music to your iPhone, iPad, or iPod in that section. Once the music is on your computer, you'll then need to use iTunes to transfer it to your device. iExplorer does allow you to transfer music files to an iPhone or iPad and save it in the correct directory inside the Media folder, but that won't update the music database necessary for it to show up in the Music app and be played back. Those files would be stored on your iPhone or iPad but hidden from view. This is due to the way that iOS works and how Apple designed it. If you don't like syncing with iTunes, you might consider enabling the option to "Manually manage music and videos" which will allow you to simply drag and drop any tracks to your device without syncing:
What makes iExplorer unique and different from iTunes is that it can transfer absolutely any of your music and other iTunes media to your computer from any iPhone, iPad or iPod while iTunes only lets you import tracks purchased from the iTunes Store. iExplorer can also import your playlists and information about your favorite tracks (the play counts and star ratings for each one). You can find out more here:
How is iExplorer different than iTunes?