With 16MB of RAM, Linux seems unlikely to be useful.

It's probably easier to think of this as a more powerful, more open, more portable Arduino with hardware crypto accelerators, a display, keyboard, WiFi, and some GPIO pins to plug in additional hardware.

They specifically mention that it will be easy to write Rust applications that run on Precursor, but it seems likely to me that there will be other options. (It seems likely that the default "OS" will be based on the Xous microkernel that they're writing: https://github.com/betrusted-io/xous-core)

Since the main processor and crypto accelerators are all contained in an FPGA, the adventurous could change the balance of CPU features that are available. It only has a single CPU core partly because of the massive crypto accelerators, from what I understand, so someone could eliminate those and have a multi-core CPU if they wanted. With 20% of the FPGA still free, it might be possible to stick in a second (maybe smaller?) core anyways? I'm not sure.