I activated a micro sim for my gs3 after 6/28 and unlimited data remained. I am not worried, I know if Verizon messes up, that I could ger unlimited data plan back, though might take some fighting. I am used to it though as verizon has already attempted to pull a bait and switch on me several times.
To answer your question, yes, you can just move the sim to a new phone, no need for activation. However, depending on the sim on the phone, you may need to cut or use an adapter. For example, rezound to rezound is a direct swap. Rezound to razr requires trimming the sim. Razr back to rezound requires an adapter.