No. After your initial backup, subsequent backups are relatively quick. During a normal backup, Mozy scans your files to detect any changes that have occurred since the last backup. Mozy then backs up any new files and all changes that have occurred since the last backup (a process called incremental backups). Because Mozy is only backing the changes instead of the whole file it saves a lot of time, bandwidth, and storage space.
For more information about getting started with Mozy, see (MozyHome / MozyPro).