Application slows down during Back up
Certainly, running a backup will have an impact on the performance profile of the machine serving the database being backed up.

For a FULL Backup, the operation consists of reading every allocated page in the entire database, and writing those pages to the backup file/device.

Since your users are complaining about the application being slow during the period of time when the backup takes place, I'd say it's obvious that the backup is having an impact.