Nope.
In the background Plesk backup will copy your files and databases and other information's silently without taking down any websites, except some small errors in end-user screen IF the user want to save something during the database backup (which is seconds), the result is data inconsistency and it rarely happens.
You can monitor your websites usage during the day (24 hour period) and find the prefect spot to schedule a backup based on your users time zones.