I'm with
@regtor ... that drive is total overkill for a backup drive and it won't make your backups any faster. If you can, I would return it and just get a standard hard drive.
These two posters know what they're talking about and I'm
not disagreeing with them, but if you can't return the drive (or an alternative drive isn't much cheaper), it should
work just fine. As they've pointed out, just don't expect it to be fast.
Instead, expect it to be slow, whether you install it inside the TC or plug it into the TC as an external USB drive. From what I've read, it seems the backup speeds are limited by the processing power of the TC cpu itself (or maybe its network interface), and not by the HDD or its interface (SATA or USB 2). But for Time Machine backup use, it doesn't matter. So, yeah, if you can return it and save some money getting a WD green or something, great; if not, there's no harm in using this drive for the TC.
Whether you want to put a 3 TB HDD inside or as an external might depend upon:
do you want to buy/get an external enclosure? (USB 2 is fine, but a USB 3 enclosure might be more useful if re-purposed in the future)
do you care about having another physical device and another power brick and plug?
do you want to bother opening up the TC, possibly breaking something? (it's pretty easy, but there's always something that
could go wrong)
is it useful to have
both the internal 2 TB and an external 3 TB connected to your TC?