Question on the fundamentals of creating a wireless network

I live in a small apartment and haven't see the need to set up a wireless network/internet connection. However, the ethernet port on my macbook gave out, and so I'm currently without internet access in my own home (Airport works fine - I've been getting online through wireless from other locations, i.e. school, coffee shops, etc.). So I'm hoping (needing) to set up a wireless network at home now. However, I know a part of that process involves a connection through the computer's ethernet port. I'll try to ask my questions as best I can. I'm just not sure about some of the basics of a network setup.

If I use a borrowed computer (one whose ethernet port works) to set up a wireless network through a router in my home, and then return that computer (remove it from the area/home), will the network remain (I think I'm asking if the created network setup remains on the router)? Will I still be able to use the network/internet connection through Airport on my own computer without that "setup" computer around? Is this not a feasible work around?

 

Thanks so much! I figured it would work alright. Haven't set one up just for myself before, and the ones I've used always had the "setup" computer remain on the network. I appreciate your (really) quick replies.