sdw will not run chkdsk on the whole disk neither will windows. it will just mount the volume and assign drive letter/volume mount point.
windows will handle a netapp lun pretty much like every other disk, if you encounter broken blocks it it will give a read error and you need to manually start chkdsk. if the MBR/GPT is broken you cannot access the disk anymore and it will offer you a chkdsk as well.
If the filesystem was found to be inconsistent and the volume was marked as dirty (can be set also manually with fsutil) before mounting, then windows will ask you to scan and fix the volume. But, if volume is not marked dirty, there is no check of the filesystem consistency. And you're right, Snapdrive is using the same mechanism when mounting a volume.