That depends on exactly what you mean by convert. You can theoretically convert anything to something else.
If you mean use the already existing circuitry to handle both transmit and receive, no. There isn't enough circuitry or power to handle both RX and TX.
Could you add a small transmitter section into the DX-100 and make it into a transceiver? As long as the transmitter section is very low power and there is room, possibly yes. Will it work well, no. The zener regulator provides only 9 volts for you to work with and not much in current.
But more so, why would you even bother? The DX-100 is a "Entry Level" general coverage receiver. It is single conversion with poor image rejection and a pretty wide 455 KHz IF. That makes for a good AM band receiver, but its not so good as the frequency goes up. It has a single RF stage to help, but on the high band it is probably pretty deaf.
I could go on about the limitations of the DX-100, but it would be better if you got a better definition of what your friend means by "convert".