It would be possible to do this, but I doubt you'd do it with less than a powerful processor.
Where i worked we used Nuance Speech Objects; they are the basis for the SIRI recognition engine at Apple.
You'd have to build a recognition dictionary of commonly used ham radio words, the phonetic alphabet, perhaps even a few call signs you'd expect to hear.
Another alternative to Nuance's product is AT&T's Watson (yes, it has the same name as the IBM supercomputers). I do not know if they would license it.
I have no idea what the per seat licensing charges would be.
Bob R - N7WY