AWOL:
I doubt 3-4 KHz would be sufficient for very low quality speech,
Why do you think that?
3kHz has been standard telephony bandwidth for decades.
The audio bandwidth could be as low as 3000 Hz (from 400 - 3400) and still be intelligible but the digital representation may need more bandwidth. I thought that 64 kbps each way was the bandwidth generally reckoned to be needed for ordinary telephone quality uncompressed voice calls using a naive encoding (for example 8 bit sampling at 8 KHz). How close you could get that to 3kbps without losing quality would depend on how cleverly you encoded (compressed) it. I wouldn't assume that an Arduino could do any clever audio compression/decompression in real time. I haven't experimented with it myself, but my guess is to get good enough audio quality out of an Arduino to make it usable (as opposed to picking words out of the static) would need nearer to 64kbps than 3kbps.