Yes, they'll carry over but they may look different. For example, if your prestige improves, you may be able to see more players later on. But you won't have to repurchase the FSS.
Another issue, (and I don't know the answer): We get a discount (10-20%) for purchasing multiple states. But, do they have to be purchased at the same time? If so, it'll cost you more money to purchase additional states later on.