I'm on the 6gb $30 plan and I did not have to do that.
I just left the old sim in my 4s and activated the new one in my 5, once the change finally went through it came up as LTE right away.
Werid a friend of mine did.
I don't get LTE here until later this year any ways so won't be able to test.. I'll call in a few days just to be safe.