Yes, you can create snapshots on Linux systems, but there is no DP integration to handle this as far as I know.
There are several different options to create snapshots based on the Filesystem type.
LVM snapshots should be File System independent because they are handled by the Volume Manager, so they may suit your needs.
Please take a look to this article about how to use LVM snapshots to take backups:
http://www.tldp.org/HOWTO/LVM-HOWTO/snapshots_backup.html
You can use DP to backup the snapshot volume instead of using TAR command.
These snapshots cannot guarantee database files consistency, so the Database should be stopped or backup mode should be enabled before you take the snapshot, to ensure consistency.
You could integrate this into DP by using pre and post backup scripts.
I hope this helps.