Yes mate, normally on o2 you keep your current sim card and just put it into the new phone, so your number would be on the iphone straight away because the number is actually associated to the sim card not the handset, but becaue your changing to an Iphone 4 they will have to give you a new sim card because it takes a new style sim card called a micro sim, which is alot smaller, you'll just get the new phone with a new sim card, carry on using your new phone until at some point usually within 24 hours the old sim will stop working and the new one, in the iphone will start, the transfer from the old sim being switched off and the new on going live should be instantanious though, you will usually just loose the signal, switch the old phone off and switch the new one on and it should register and be working immediatley.
The shop might tell you to turn both of them off for 24 hours or something whilst they transfer them but thats normally them just covering their backs incase there are any delays, its usually pretty much straight away.