There are two aspects: physical and electrical connections.
From the physical side the answer is no, because the Audio Pack has two 20 pin sockets. Now you could imagine to solder pin-headers onto the Pico W of your NFC-reader, but that is not possible, since the Pico W is soldered flat onto the support PCB. So what you could do is solder wires directly to the Pico W, but that is not without challenges.
From the electrical side of things: again no. How could you find out? You have to download the schematic of both devices and check which pins are in use. The Audio Pack uses GP9-GP11 and GP22. And the NFC device uses even more pins (and all of the ones that the Audio Pack needs).
“Half-decent quality sound” heavily depends on the speaker. The one I use in the above project is definitely not good (far too small), but I had to make compromises.
This is incredibly helpful, thank you. In this picture I can see you’ve soldered little header pins to specific GPIO pins to use the Dupont cables - I’m not sure what phrase to use to search for these, what are the little solderable bits called?
My project is pretty simple - play audio files off the SD card when a given NFC tag is touched, think this may just do the job.
These header pins are called header pins. You will have to solder them to the throughholes left and/or right of the Pico-W. You can find them here in the shop (or everywhere else, just make sure you buy the 2.54mm spacing variant). Break Away Headers - Straight