It is possible you received a warning telling you that you don't have the rights to execute a job on the destination server and that the User alert emails will be sent if you continue. This can happen as a warning in the pre-check report with the following message:
- You don't have the server side permission required at the destination to prevent the User Alerts from being fired during the copy.
User Alerts are disabled after the item is copied so you are not spammed with unnecessary alerts. They are enabled once the SharePoint timer job ran. This job is executed every 5 minutes out of the box, but can be manually changed.
To be able to copy alerts without receiving any email, the user at destination must be Farm Admin of the destination server.
If you choose to copy alerts anyway (by keeping the option checked), what happens is that users that configured alerts on items will receive a notification by email when those items are copied. The User alerts will trigger to tell them that their item has been created at the destination.