I just got an ESP32 board the other day so I will be testing it soon. 

If you use the NodeMCU firmware for the ESP8266, then there is a simple function to generate sound with Lua:

https://nodemcu.readthedocs.io/en/master/en/modules/pcm/#sigma-delta-hardware

Of course, the output signal needs to be amplified to drive a speaker. One of these boards would work for a normal 8 ohm speaker:

http://cgi.ebay.com/172438970072

I have some of it. I don't understand how they can make money with this, $0.99 and free shipping, that's crazy. One LM386 at Digikey costs nearly that much, but then you have to pay much higher additional shipping cost as well. But if this works, just the IC could be used on a custom designed board, together with the ESP8266 module, the buttons, and the LCD display. It is just for hobby, so minimum cost doesn't matter, but you can get single LM386 ICs from ebay, too.

BTW, I have this morse paddle:

It is waiting for your Lua program to use it with my ESP8266 :-)

currently I am using the output from an UNO with the speaker connected thru a capacitor. on an unrelated note it would be nice to have the 16 megabyte versions of the ESP8266 boards supported. 

So how do you plan to do the hardware? I just tested a new ESP32 module and NodeMcu with Lua works fine on it (there is a dev branch on the github project where the team is porting the project, I compiled it from source and WiFi works already). One nice thing about the ESP32 is that it has an integrated 8 bit DAC, so you don't need the external DAC IC as seen in the Arduino project to create a nice sounding beep output. But it needs quite some power, with WiFi running about 110 mA at 3.3 V. But this would be no problem, if you use an external power supply, like an USB power supply wall wart and add a USB micro socket to the board.