The Commodore 128 has two CPUs. One is some variant of the 6502, and the other is a Z80. One CPU is there for compatibility with the Commodore 64, and the other is there presumably to give basic compatibility with the CP/M titles that were available at that time. My question is whether those two CPUs can run at the same time, both accessing memory and the graphics and sound subsystems, or if one has to be disabled or halted while the other runs.
No, they cannot.
They share both the data and the address bus of the C128, so they can only run exclusively at any one point in time.
The address bus is apparently directly connected, the data bus of the Z80 through a set of latches to the data bus of the rest of the system.
In CP/M mode, the 8502 is handling keyboard, screen and printer and serial ports, while the Z80 "runs the programs". While one CPU is running, the other one needs to be HALTed.
The 8502 CPU was also there for C128 mode, of course.
The 8502 and Z80 cannot be used at the same time. There are however other options.
The C128D has a third CPU, a 6502, in the floppy drive. Any drives connected to the IEC bus port of a C128 or C128D also have a 6502 in them. These CPUs could be used in parallel. A 1541 or 1571 has only 2KB of RAM but a 1581 has 8KB of RAM. The less common 8050 and SFD-1001 have 4 KB of RAM.