No. Once you have launched SDK/TF2 for verification at home (You have to start offline mode while Online, BEFORE you leave for school), quit them and then tell Steam to restart in offline mode. If it works, Steam will quit and re-open but with say "Offline Mode" at the bottom of the screen. Once this happens, you know it's set up right. You can THEN disconnect from your home network, exit Steam or turn off your computer if you need to, and it will still come back in offline mode at school.
Offline mode just tells Steam to not connect, but you have to set that up while you still are connected (I know it's frustrating when I forget to go offline an I'm stuck with stupid "Cannot be done offline" errors all week).