I have a Mustang I. The headphone output is also the line out. I plug a 3.5 mm to 1/4" cord into that and my Focusrite Saffire. Works fine.
Does the III have a Phones output? It should work... but then you would probably encounter latency issues with the RealTek in MME mode. I'll even go out on a limb and say you will encounter latency issues.
You can still use Fuse to change presets or load new ones into the amp from the internet, but maybe not at the same time as when recording.
Welcome to the forum.