Hi DJB,
This will quite possibly work. There are some reasons it may not work reliably:
- The PICO-D4 does still require some external components, notably power supply capacitors (see Section 7 "Peripheral Schematics" in the datasheet). You might need to find a way to solder ceramic caps directly to the breakout board, to keep the overall series resistance & inductance as low as possible.
- The antenna connection needs to reliably send and receive 2.4GHz so usually it's an controlled impedance feedline. The breakout just has a regular PCB trace connected to the antenna pin. But if you can solder an external 2.4GHz antenna then it might work well enough for a very strong Wi-Fi signal, anyhow...? There is some small risk of damage to the RF amplifier due to the (likely) large impedance mismatch.
Overall soldering a couple of capacitors and some wires directly to a WROOM or WROVER module breakout board will probably be more reliable and not that much larger (although these breakouts can also be unreliable as most of them don't have enough capacitors on the breakout.)
If you decide to have a try with the QFN breakout, please post your results!