Nope.
Echo is the primary sound followed by a reflection of that same sound – delayed in time.
Phase cancellation, by definition, is adding two copies of the SAME sound together with one of them delayed EXACTLY 180 degrees out of phase with the other.
That process has NO effect on sounds that are already naturally delayed like an echo. The echo is, by definition, a separate sound from the initial sound the echo resulted from.
As a technique, it’s valuable in something like balanced audio lines, where you have three wires, one carrying the signal, the other carrying nothing, the final wire the ground. Then when the CABLE picks up RF noise, you can take the whole signal – invert the phase – and mix the result back in – so that the NOISE picked up equally by BOTH conductors is cancelled out. But it only works because the noise you’re canceling is DIFFERENT from the signal you’re interested in passing.
The only way an echo is “different” is that it’s shifted in time. So the traditional way to TRY and compensate is to set up a gate so that you allow the primary attack of the word to pass through and then gate the circuit shut before the echo passes.
Often, that’s an “iffy” solution since you often get a mixture of the echos and the next wanted sounds in actual content.
There are also more sophisticated forensic audio tools that mathematically kill sounds below the threshold of amplitude of the initial attack sound.
But in reality, audio usually a lot like paint. Once you mix two of them together it’s pretty hard to “unmix” them. At least unless there’s something very distinct about the sounds you want to remove compared to the ones you want to keep.
Good luck.