broadcom doubt

Hi,
I have a doubt about the need to install the broadcom drivers.
My laptop uses a broadcom wifi card.
I have booted the Alpine iso and ran setup-alpine.
After selecting wlan0, it recognizes and list correctly my ESSID point, but later the sender doesn't resolve DHCP.
My doubt is, if the system did find my ESSID point, doesn't that means the connection is working even if the broadcom driver is not installed?