Well it'll do that, however performance won't be great and for backup it's not the most elegant solution. If you're willing to scour the second hand market for an old PC for similar price or invest a little more you can build a PC and stick something like FreeNAS on it. FreeNAS is free as the name suggests, needs naff all resources to install and supports Software RAID aswell as FTP,HTTP,SMB,iSCSI,TFTP and any other way to get files to and from it you can think of. With regards to backup, it also supports rsync. Rsync is ideal for home backup really. You install the client service on the laptop and as files change within the specified directories it updates the changes with the server in background.
In short a PC with FreeNAS type OS isntalled + some disks is lots more flexible and faster than an off the shelf soho NAS box.