Samsung Galaxy S2 — Am I correct in thinking?

Right just want to check something and make sure i'm not going to run up a huge phone bill.. just as a warning I'm not the best with phones and computers.

Basically I have a laptop which the wifi has failed and so I can't connect to my router. So in a moment of genius I thought I can tether my phone (galaxy s2) which is connected to my home network and this will get m computer on the tinterwebs at least till i get a new wifi card.

So i turned off data network mode:
settings > Data Usage > Mobile data > Off

Am i correct in think my phone will now not use 3g etc for the internet?

If i then connect to my laptop via usb tether
Settings > More >Tethering and portable hot spots > USB Tetherherin > ON

and within network settings on my computer select my samsung and the internet works am I correct in thinking my phone is using my home internet and allowing my laptop to use the internet without going to cost me a fortune / use up all my data plan ?

Thanks