Yes it is snapshot-based - it uses SnapMirror from primary to secondary. So if you've already got local snapshot policy in place on your volumes, then there is no additional overhead. NDAS takes the daily labelled snapshot off the secondary and sends it to cloud. Your existing local volume snapshot policy on the volume will be used on the primary.
If you start to protect volumes with NDAS which don't have a local snapshot policy (e.g. if you'd disabled the default ONTAP snapshot policy for some reason), then NDAS applies a default policy which is the same as ONTAP's default policy - Hourly snapshot keep 6, daily snapshot keep 2, weekly snapshot keep 2. So those will consume space on the primary. As you know, ONTAP snapshots are space efficient so that only the changed blocks take up real space.
The NDAS interface in the Data Protection screen tells you what protection is currently in place for each volume - represented by the green shields. 