It's not possible with the default setup for two reasons:
- The TDO signal coming back from the FPGA on your Cyclone III board will conflict with the TDO signal from the external board
- If the on-board blaster detects that a cable is plugged in to the jtag socket then it will disable itself
You can probably work around both of these with clever setup on the analogue switches / links on the board, and with care about what you do to pin 2 and 10 (I think) on the cable. If you do get the board set up so there are no conflicts then you may have issues with signal integrity due to large capacitive loading on TCK/TMS/TDI from the original board.
So not impossible, but difficult to do properly, which is why this sort of use is unsupported.