A:
In short, YES!
In long, if you are using Mac, just format to OSX Journal not case sensitive type and use it as time machine. I would use 'airport express' to do time machine backup wirelessly for 2 reasons, its wireless and convinient, and also because its an external hard drive with external power supply not a portable usb hard drive, so they are more delicate and should not be carried around.
For PC you can use a program of your choice - crashplan free version will do it for you, you can also back up your other computers to the same HDD using crashplan free program. You can also go wireless or NAS route if you have a NAS system or appropriate router.
Hope it helps!