Yes, but a designed-for-FPGA SHA256 implementation looks very different than an ASIC SHA256 implementation - the ASIC has far greater routing flexibility and density, and can therefore use far more combinatorial logic between register stages.

(ASIC simulation on an FPGA will retain the combinatorial stages but run at dramatically lower fMax)

Yes, hard silicon will be another magnitude more performant than FPGAs and GPUs, but ASICs properly take on negative value when they're no longer profitable to mine with. (Note that efficiency won't be much better at the same process node. You can just pump more power through each ASIC die)

Edit - I misread your comment. ASIC designers will use FPGAs to test their design but it won't be optimized for FPGAs which have a different logic-and-memory characteristic than ASICs. There aren't many great SHA256 FPGA implementations, largely because there's not that much demand for one

Unfortunately I think most of that innovation happened behind closed doors, because everyone wanted to maintain their competitive advantages.