yes, that is pretty much what i am suggesting.
if the drive in a redundant raid array fails (raid1, 5, or 6), the array will continue working as if nothing changed. The only noticeable difference to you is that it will be slower.
Depending on your drivers, controllers, and setup, it would notify you in one of many different ways (aka, it all depends on what setup you use). Performance will be low, but it will work.
If you use a NAS and don't want to manually check it via a monitor, then you can set it up to notify you via email.
GigaBIT ethernet allows a max speed of 125 megaBYTES per second. (bit is 1/8th of a byte). So it should be plenty fast, your computer's speed is more likely to be a limit in the NAS.
The 300+$ controllers have the speed advantage, but not the safety, or reliability, or flexibility (aka, it is a single point of failure, where you need to get the same model and use their own method to reaquire the array if it fails, if the nas fails, you repair it and the data remains)
Do you already own drives? because you, seem to be mixing different sizes there (1.5TB and 1TB). which is a bit odd to do. why not one raid6 array of 7 drives?
My NAS is an open solaris installed on an old 160GB IDE drive with a 3450 (20$) video card in an old nfroce 5 mobo with a new X2 BE (best efficiency) 2300 CPU and 4GB of ram.
with 5 SATA 750GB drives in RAIDZ2 (raid6) which gives me the space of 3 drives, and the ability of two of them to fail without loss.
I would like to point out that backups should be targetted at CAUSES of data loss:
1. Fire - offsite backup
2. Flood - offsite backup
3. FBI (a competitor places an annonymous calls the police saying you traffic guns or CP, they will confiscate your computers forever if you are charged, if you are NOT charged they will give them back after a mere 27 year holding period.) - offsite backups
4. bit rot - use a checksuming filesystem (only ZFS at the moment)
5. Cosmic rays bit flipping - use a checksumming filesystem (only zfs at the moment)
6. Drive failure - use redundancy
7. Controller failure - use a scheme that allows you to replace the controller (aka, NOT a motherboard... except for RAID1, raid1 is fully portable even on mobo controllers)
8. A controller failure with a controller no longer available on the market - use a system that allows you to switch to other controllers (aka, OS based software raid like in linux, solaris, windows server, or open nas).
9. Theft - offsite backup OR worthless media backups (DVD-R)
10. Virus - NOD32 antivirus

, but if not, have an external backup that you unplug except for when you manually connect it / turn it on to perform a backup. (not that i have seen a virus that just deletes data)