If there is short term immunity yes (diphteria, tetanos is an example, polio too). Being exposed to the same antigen while you have an immunity should reactiva

If there is short term immunity yes (diphteria, tetanos is an example, polio too). Being exposed to the same antigen while you have an immunity should reactivate this immunity, that's a reason why a "herd immunity" tactic could work, at least for a time However if the natural immunity w/o reactivation only last a year or less, you will end up with a new outbreak at the end of the period. And if the immunity period is shorter than the recuperation one, you will have a virus that will be a lot more lethal.