I'm thinking no, that you need a TW-523 or PSC05, but wait till someone else agrees with this statement before you run out and get one. :D
The ELK-M1 does not interface with the CM11A. The TW-523 or the PSC05 can be used for the 2-Way X-10 interface (the M1 transmitting and receiving the powerline commands). The TW-513 or the PSC04 can be used if the M1 is only going to transimit X-10 powerline commands.
The cm11a is a serial device. The TW523 and the other X10 interfaces are opto coupled and not serial in nature. I too would say it would not work.
That's right, the CM11A is a serial (RS-232) device, while a TW-523 is a TTL-logic level device that uses direct hardware timing, and has no relation to anything resembling a serial data stream, baud rate, or other protocol. It ouputs a two level square wave indicating the zero crossing of the power line, and the other two signals indicate (or enable) a signal to control a burst of 120 kHz signal on the power line.

They could hardly be more different.