No. It has a firmware bug that will cause it to unmount without warning and only remount with a power cycle. You can reformat it for OS/X, sure. And it will work while it is awake. But you're better off going with another manufacturer for OS/X as Seagate does not support OS/X properly.
I haven't tried this one personally, but other reviews have stated that it works. Generally, with drives like this, you have to open Applications > Utilities > Disk Utility on your mac, then re-format the drive as Mac OS Extended (Journaled). From there, it should just work, even with Time Machine.
Working flawlessly attached to our Time Capsule backing up an iMac and 2 MacBook Pros. We simply reformatted to Mac OS Extended (Journaled), connected it to our Time Capsule, and selected it as the back-up disk through Time Machine. That simple. Very happy with this external drive in our Mac-only ecosystem.
It works fine for me too. I have tried it directly and thru my network(hard drive connected to my router.) It's quite fast so most of the time I copy my files directly to the network drive and then pull it into my Macbook to watch or edit it.