Yes, it is possible to add a second hard drive to a mac IIcx internally. This
is definitely not a recommended procedure by Apple but I have done the equivalent to my CX after upgrading it to a Quadra 700. The power supply is still the
stock CX's and it was able to power two Quantum LPS drives, a PLI SCSI 
accelerator, a Micron technologies 24 bit video board, Daystar QuickCache,
New Technologies Overdrive and 20 meg of RAM simultaneously.

I added a new mount for the drive by attaching angle brackets to the drive
tower. The internal SCSI cable was changed to a longer flat ribbon cable onto
which I added an extra connector about midway. The final HD was internally
terminated and the drive between the motherboard and final HD had its terminator resistor packs removed. Cooling has not been a problem and no SCSI problems
occur with either the PLI SCSI chain or motherboard SCSI hooked into the two
internal hard drives.