You should be able to keep the audio signal coming out of your iPad and going into your Mac entirely digital. There are at least a couple of ways to do this.
It looks like if you have El Capitan, you're golden. It has a feature called Inter-Device Audio, which will recognize your iPad (via the Audio Midi setup) as an audio device, allowing your DAW to recognize it as an audio input. Whether GarageBand will do this, I'm not sure. But it seems to work for Logic. Here's an article with an accompanying video: http://audionewsroom.net/2015/10/how-to-record-your-ios-device-into-your-mac-daw -on-ios-9-os-x-10-11-welcome-inter-devic…
Another way is to do this is to use the app MusicIO. You connect your iOS device via USB to your computer. It requires the app on your iOS device ($10 in the app store), and a server and plugin for your Mac (a single, free download from the MusicIO website). I use it for both listening to audio from my iPad through my desktop Mac (which has high-quality monitors) and for streaming audio into my DAW (Digital Performer in my case). You can also use it to send MIDI back and forth between the iOS device and a DAW. It takes a bit of practice to get it set up correctly. (My advice is to set it up the audio in the following order: 1) open desktop MusicIO server 2) connect your device to your computer via USB 3) open MusicIO app on your device 4) select which music app you want to use as a sound source and then open up that app [from inside the musicIO app]).
It works... okay. I have eight apps that are supposedly able to work with MusicIO -- they're listed under "available instruments" inside MusicIO. But it actually only works with four of them. But that's okay with me; those four are the ones I really want to use with this app. The degree to which it works well varies greatly among these apps. It works flawlessly with Finger Pro: MoDrum. With SugarBytes' Egoist, the play button seems to disappear and there are only limited ways to play back loops and sequences. But the audio seems fine. With Elastic Drums, there seem to be quite a few audio glitches and even slow downs in the audio playback.
I think how well it all works can depend on how the app developers implement IAA. More about that here: https://musicio.zendesk.com/hc/en-us/articles/204364768-Does-Music-IO-support-Au diobus-Or-Inter-App-Audio-
Even though it doesn't work uniformly for all apps, it was a worthwhile purchase for me. There's nothing like hearing the audio over $600 monitors as opposed to the teeny speakers on my iPad. And it's a much cheaper alternative than some of the hardware interfaces designed specifically for the iOS devices. I'm hoping that some of the problems will get ironed out with future versions of both MusicIO and the music apps.