Will the Kestrel-3 Family Run a Protected OS, such as Linux, BSD, or Plan 9?

I doubt the very first model will. The FPGAs I'm targeting are relatively small by RISC-V processor standards. I doubt they'll be large enough to contain an MMU-enabled core with FPU and all the bits needed to make the rest of the Kestrel-3 work.

If, however, by some miracle I'm able to fit an MMU-equipped Rocket-compatible core onto the FPGAs accessible to me, this would of course accelerate the effort to get a "real" OS working!

Otherwise, eventually, yes; I intend that a suitably expanded Kestrel-3 be able to run Linux, BSD, or a port of Plan-9. What does "suitably expanded" mean? Hopefully, in the not too distant future, I can build a Kestrel-3 computer using a commercial RISC-V processor; or, maybe someone can make a CPU plug-in card to serve as an adjunct CPU to the core residing in the FPGA. Options exist, and will be evaluated when the time is right.

Regardless, I will not invest the effort to perform the port myself. Porting these operating systems is a huge undertaking, requiring substantially more effort than it takes to design the computer in the first place. Hopefully, though, a community will have evolved around the Kestrel-3 family, and if someone's willing, they'll undertake or coordinate the task of porting.