No. Any sessions that are active when you publish will stay active until the user disconnects. When publishing, only unused instances will be retired after the new instances are created. For instances in use, they will only be retired after the user(s) disconnects.
Note that the process of publishing will always create new instances that are powered on once created (and therefore you will incur a one-hour increment of usage for each instance as set by your fixed or maximum capacity setting).