When I did this with my 5s, I didn't have a SIM to move over and it didn't activate properly, so I had to call Verizon. The group that does activations is completely separate from the one that does plans, and she assured me that nothing was going to change with my plan, that as I didn't use the upgrade I would keep my unlimited data. Everything worked fine once we got it activated and no plan change happened.
So, basically, don't worry too much if you do find you have to call them.