Yes, if the change involves getting more tickets (personal plan to plus one plan), then it will be treated as an upgrade. The change will go into effect immediately, and you will be able to use the additional tickets right away. You will be charged for the difference between your old and new plans upon upgrading and will start to pay your new rate when your plan renews.
If the change involves you getting fewer tickets (Plus one plan to personal plan), it will be treated like a downgrade and go into effect on your next renewal date. You can continue to use the remaining events of your former plan until then.