Leaf blowers will lift and blow wet leaves reasonably well. The challenge comes when there are multiple layers of wet leaves stuck together. The best way to manage this is to keep on top of clearing leaves and not allow the debris to build up.
When clearing wet leaves, it will be easier to blow and clear small areas as you go, rather than blowing all leaves into one pile which will eventually become too heavy to move.
Certain blowers are supplied with both round and flat nozzles. The round nozzle is good for clearing dry leaves as it moves a larger volume of air over a larger surface area. The flat nozzle concentrates the airflow into a blade, increases the air speed which helps lift wet leaves.