I'm pretty sure the program ROM for it is only visible to the Z80, not the main CPU. You might be able to somehow trojan it out, but that would require finding/exploiting a bug in it.
The Z80 on the Rainbow comes up in reset. The 8088 has to put its program in it, and take it out of reset. The boot roms are mapped only on the 8088 side. In fact the only thing the Z80 is attached to, apart from the shared memory and the 8088 interrupt line is the floppy drive.
But I also have Z80 compilers and assemblers if that's helpful. I didn't see anything on the prints, though, that could easily be read back from the Z80, with the possible exception of the Z80 memory arbitrator PROM, though that's a long-shot at best given the machinations one would have to go through to toggle the different address lines and chasing down where they all go... I'm not sure they all go to something that's readable by one or the other of the CPUs.