Good question. In principle one can bounce radio waves off a CME. However, close to the Sun the plasma turbulence and high collision frequency would make a really awful reflector, and then you will be looking at it against a strong noise source.

Further out in space the electron density drops below that of the ionosphere, so nothing groundbased will see any echo. With the low frequency an enormous orbiting antenna, or one on the Moon will be needed. It could be that we will need to put one of those radars on the Moon at some point.

Otherwise, one can detect CME's with radio telescopes. As they pass between us and quasars we see them twinkle, like looking through a heat haze. This method though has not yet proved or has been made sufficiently reliable to justify the expenditure on a committed system. things could change.