I think it is possible but I am not sure if it will actually work. I asked the creator of ZXBaremulator, a ZX Spectrum emulator that runs on different versions of Raspberry Pi and it is almost like having a real working device, but unfortunately he replied that the model used for PicoCalc is not compatible. I am searching for other solutions and I am hoping that someone could eventually make this work properly. I also asked if another emulator called M.CU.M.E. would work on a PicoCalc. The response was that I would configure the firmware of the PicoCalc in order to make it work. Maybe in the future there will be a Raspberry Pi Pico ZX Spectrum bare emulator that will work on the PicoCalc.
the main issue you’re likely to run into is the added overhead of integrating the spi driver for the LCD screen and the i2c scanning of the keyboard
emulators on pico are usually very tightly coded to squeeze performance out of it, and there might either not be enough left to do those things, or they’ll be hard to integrate