It should work just fine. Actually, I don't think it's necessary to Jailbreak in order to do what you want to do. However, if you want to Jailbreak for other reasons, it certainly shouldn't cause any problems.
The only concern I can think of is, depending on her old phone and her cellular plan, she may not pay for/have access to cellular date, AKA the internet on her phone. All that means is that getting on the internet(via iPhone) without updating her plan will trigger very expensive fees.
Unless you buy it from a 3rd party source (ie. eBay, Craigslist) then you're going to have to subscribe to the data plan. But, if you were to buy an unlocked phone then it would be as easy as taking her SIM out of her old phone and putting it into the new iPhone.
They will make you activate it if you buy it at the Apple or att store and for the iPhone contacts aren't stored on the sim cards. Also, be very careful about not getting a data plan as the iPhone hogs data and you could get a $14,000 bill if you are not careful.