Yes, the IMAP access is necessary to run GMail Backup. If you don't have the IMAP access, you will get the following message:

Error: IMAP: [ALERT] Your account is not enabled for IMAP use. Please visit your Gmail settings page and enable your account for IMAP access. (Failure)

You can see more at //www.gmail-backup.com/incremental-backup#comment-164