The dock lets you program AFMA values directly into the lens with the added benefit of setting corrections for multiple distances, unlike the AFMA settings in the body. So if your Sigma is good at minimum focus distance but is off at longer distances you can program in multiple AFMA corrections, unlike body-based AFMA where you have to split the difference or just optimize at one extreme or the other. If you use the dock to perform AFMA you would typically disable in-camera AFMA for that lens (set it to 0).
The big down-side is that you can't currently set AFMA corrections for different bodies (addressing the OP's question), so you would either need to use body-only AFMA or a combination of lens and body AFMA in that scenario.
The other annoyance is that to use the dock for AFMA you have to shoot, unmount the lens, attach the dock, make adustments, remount the lens, re-shoot, and repeat. Pretty fiddly compared to using tethered shooting with the EOS Utility or Focal.
That said, the dock also allows you to update the firmware in the lens to correct performance or compatibility issues that are identified after shipping. For example, there was a firmware update for the 35 Art last year to improve AF reliability and noise. That feature of the dock could be important long-term if Canon tweaks their EF communication specs in future cameras, since 3rd-party companies have to reverse engineer those specs and things could break. I bought the dock for my 35A even though it doesn't need AFMA on my 6D, and it's been nice for the firmware updates alone and as an insurance policy. It's not expensive, but it would be a great item to share around with friends or a photography club since it generally sits unused after you tweak your lenses.
Hope that helps. I have the dock and software, so let me know if you need any specifics and I'll check tonight.