normally rsync doesn't need the other side to have rsync installed..
you can use it with rsync server and rsync client mode but it is not needed..
you will however need ssh access to the NAS..
as pir suggested you could also use FolderSync which has a nice Tasker plugin..
all my backup to my internal network I do with rsync because it's really powerful.
Backup certain things to Dropbox, I do with FolderSync (but it also has FTP, SMB etc..)