No, the music has to be on your computer first, and then it can be synced to your mobile device over wifi. If you'll have Spotify open on your iPad and computer at the same time, your iPad should show up on the computer in the left-hand sidebar under devices. Click on it, confirm that you want to sync to that device if asked, and you can check the option to sync local files...however, this method is only good if you have enough space for everything.
The way I sync to my Android, since I don't have enough room for all my local files and also want to have more control over what actually is transferred, is to just put the tracks I want onto their own playlists and sync them to the phone. I create a playlist for each album that's not in the Spotify catalog, but you could also just throw everything into one big playlist.
Here's a screenshot of how I have mine organized:
You can sync either through the computer or the iPad. Just remember the key is to have the app running on both devices, otherwise the iPad won't see the local files.
