I've noticed that on my OSX macbook the connection time is slow, but it seems to connect before you log in if it's asleep. I think Apple uses tricks like this to make it seem much faster.
I'm running Archlinux from a flash stick on a cheap Haswell Celeron. From BIOS to chromium/wifi on is about 20-30 seconds. And I'm using connman so it could be faster with directly using wpa_supplicant/dhcpcd. On Windows it took up to two 2 minutes. So it is definitely an issue with hardware and drivers not Linux in general. Also using old hardware (including old wifi dongles) is a recipe for headaches. A cheap Haswell laptop or a desktop coupled with Linux friendly wifi dongle or a card should work fine.
