Yep, you can change your promo packs anytime, but the effectivity will be on your next cut-off date. That's it's highly suggested to change your promo packs nearest your bill cut off to ensure that you maximize usage of your promo pack.
Changing near the cut-off date is also recommended to avoid being charged for two overlapping promo packs. (Opting out of a promo pack mid-cycle and opting in to another one at the same time means you pay for both promo packs in full since they overlap mid-cycle.)
As soon as you enrolled in a new promo pack, you can start using it immediately. However, there may be delays in reflecting the change when checking your plan's unbilled charges. But don't worry since this should normalize once you receive your bill.