I have not seen any official statements regarding this question, or any attempted 3rd-party tests, so I can't really say.
As the SSD card is mounted to a socket that is unique to one of the GPU cards, the SSD would not be usable with that card removed. Assuming the machine can function with only one GPU, you may also need a bootable external drive in that case.
However, I am also wondering if this is a realistic concern. While some MacBook Pros have had GPU issues, they don't seem to be because GPUs are a problem, but rather the specific design seems to have a weak point. Beyond that, I have not heard of GPUs being a problematic component. In my experience, power suppliers are much more problematic.
That said, I would love to see a consumer-oriented version of the Mac Pro, with a quad-core i7, single GPU, and internal HDD with Fusion Drive, at a much lower cost. For headless Macs, there is a massive gap between the Mini and the Pro!