Yes, anything in place before the fork will be recognized by both chains. You can then make transactions on either chain, and the other will go on as if nothing has changed, still recognizing the coins in their original address.
Realistically, the total value of these coins may change or it may not. One chain will likely dominate and have most of the value. But the total value may increase, decrease, or (unlikely) stay the same.
Total value could decrease if e.g. people feel that the fork demonstrates a weakness in cryptos. It could increase if the disagreeing parties are both satisfied with their forked chains and both have utility.
Realistically, the total value of these coins may change or it may not. One chain will likely dominate and have most of the value. But the total value may increase, decrease, or (unlikely) stay the same.
Total value could decrease if e.g. people feel that the fork demonstrates a weakness in cryptos. It could increase if the disagreeing parties are both satisfied with their forked chains and both have utility.