They should. I have currently AMD + NVIDIA GPU in my PC, the lanes are split on the motherboard (it can be 1 x16 or 2 x8).

There is a bit of fiddling with drivers but it is possible to have one manufacturer working in compute only mode and other as graphics and compute.

If you think regular GPU drivers are shitty, then wait until you try to install both AMD and nVidia drivers at the same time. It's not very stable, to say the least (Windows 7). Never tried it since. Not worth the hassle.

Take a look at the hashcat link I posted above. Someone had success with a mixed AMD/NV setup using linux.