So I managed to successfully install Ubuntu and get everything working except wireless.
I do not have an Internet connection, but I can retrieve files from the Internet via use of my OS X partition.
I used b43updated.zip from this thread: No Wireless When Install 14.04 on Macbook Pro. I can see "Connect to hidden connection" and can toggle wireless, but no networks appear in the list.
Output of lspci -nn | grep 0280:
02:00.0 Network controller : Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN controller [14e4:432b] (rev 01)
I'm also using Ubuntu MATE at this point, not Ubuntu.
I've also managed to get the Wi-Fi networks to show in the network list, but not to connect.