It seems that there is almost zero information about the wireless chipset for the Pi4 on the internet, at least that I could find after more than an hour of searches. Ultimately, I decided to etch Raspbian onto a card and put it in a Pi4 and checked out dmesg.
Raspberry Pi 4 uses the brcmfmac43455-sdio driver. I copied the driver from Raspbian and put onto my card with piCore 11.0alpha1a. Put the piCore card back in the Pi and now I have wifi!
Worth noting that I had to also reconstruct the wireless-KERNEL.tcz file to make this happen as well.
In any case, I just wanted to verify that wifi on Pi4 works in the new piCore alpha for anyone else trying to do this.