Hi Dustin,
You can indeed push audio between the Android device running WoAD and the radio, using AFSK, 1200bps.
At its most primitive you could place the phone close to the radio handset, adjust the audio levels on both sides, and you'd be good to go. The reason not to do that would be background noise, having to enable VOX on the radio, etc. Its not an elegant solution and very prone to all kinds of problems.
Better than that would be to use an audio cable between the phone and radio. This isn't recommended either as again you'd have to use VOX and are likely to have problems with ground loops and hum and noise on the cables. My electronic knowledge doesn't extend to the potential risk you're putting your equipment in when you directly connect them in this way.
The proper solution is to use a couple of audio isolation transformers and additional circuitry to trigger the PTT so you don't have to use VOX on the radio. This is what the VoxBox and easy-digi do. The circuitry used is simple and can easily be built by an electronic hobbyist.
I don't have an IC-705 but a quick look at the manual doesn't suggest that you could use the WiFi for what you're trying to do. The bluetooth may be able to achieve what you're after, and would involve making the phone think the radio is a bluetooth headset, or vice versa. This would likely involve some extensive reading of the manual of both devices, but may be possible. WoAD would still be running in AFSK, 1200bps mode but would now be sending and receiving the audio signal over a bluetooth connection.
Hope that helps,
Andrew
VA7YAA