Does Itunes Need To Be Connected To Internet To Activate iPhone 5s? (W/ Sim Card)

Hello, I have recently received an iPhone 5s. I did a bunch of research to try and activate it without a sim card and ended up purchasing one with a phone plan. I finally got the sim card and activated it over the phone with its service. I restarted the iPhone after inserting the active sim card. After selecting the language and country, I attempted to activate the iPhone. Of course, it said it could not be activated with cellular data or whatever (it showed my connection and that I had 3G data on upper left corner) and it still did not work after several attempts. After that I tried plugging it into iTunes. Well...instead of saying to insert an active sim with no PIN lock.. it said I need to make sure my network is active to activate my iPhone..

****So My Main Question Is. Does My Laptop Need Internet Access To Activate My iPhone 5s Through iTunes?****
P.S. iTunes is up-to-date.

Thanks for all respones and help in advance...sorry for all the details, I just would like an accurate answer please.
-Little Kurt