I assume this is more complicated than just converting analog audio to digital, as the host-to-device relationship connection would need to be made between the guitar processor and the Arduino as well; and I believe this relationship connection is where the complexity lies.
The bad news is, you're right... On the host side there is a driver that communicates with the firmware in the USB device. I assume you installed some software for the Helix and that installation probably included some drivers. Windows and OSX come with some standard drivers and "class compliant" USB audio devices work with these Microsoft-supplied and Apple-supplied drivers so you don't have to install a driver because it's already there. I don't know about iOS.
I'm kind-of lost with your signal-flow and overall analog & digital "ins & outs" but I think you'd run into limitations with the Arduino. It's not fast-enough to do "complex" DSP (digital signal processing). There is no DAC (which you may not need with the Helix) and the ADC is only 10-bits and it's only accurate to a sample rate of 15kHz (which limits the audio to 7kHz. That might be "good enough" for guitar but it's 2018 and I'd say you ought to be using at-least "CD quality" (16-bits, 44.1kHz).
You might look into the [u]Raspberry Pi[/u]. it's got a built-in "soundcard" and a USB port. But drivers for the Helix might be an issue, as well as processing speed depending on how much processing you want to do.