Does the iphone stay connected to the internet if you start an application and it locks?

okay so i have an lg shine right now...and my carrier is at&t; and i am thining of getting an iphone on ebay new....i heard if you got an iphone your phone carges will be higher is this true in my case??? or it will just be the same phone bill as i have right now wich is 140 bucks a month??? ________________ unlock iphone 3gs 3.1