No. According to flashhavoc's TT685S announcement, you can only set a TT685S to Groups A-C.
This is also the case for the Nikon, MFT, and Fuji flavors. That is, everyone but Canon.
Only the TT685C can be set to groups D & E, and that's because Canon cameras can actually set Canon flashes to groups A-E. I suspect that Godox gear is reverse-engineered from Canon tech, and then adapted for the other systems. The fact that my TT685C can also do TTL ratios, but I'm pretty sure the other flavors don't is another indication of this, as is the changing backlight color for slave/master indication (which is how the Canon 600EX-RT does it).
The optical wireless flash systems that are used by everyone else are mostly limited to three groups (A, B, and C), and since that's all the camera can communicate, that's all that Godox has to work with. The only exception to this would be Nikon's new radio system, which allows for six groups; and Sony's new radio system which allows for five. But they've only reverse-engineered Canon's camera menu/flash communication protocol.
I think this is also why the non-Canon system flashes sometimes have to be set to TTL on the flash to allow for remote power control, even in M ratios.
Godox, of course, can build groups D and E into its own lights that don't have to ever communicate directly with a camera, but only a Godox transmitter. My Godox A1 can also be set to groups D&E as a slave.