Can this WD 2TB HD drive fit?

You have two issues here the first is the hight of the WD is too high for your system.

The largest you can put in which is very tight is 12mm. I don't recommend it as you are flush with the case bottom. The ideal drive would be a 9.5mm. This is one of the few HD's this large: Samsung Spinpoint M9T but its a SATA III drive.

The second issue is your systems SATA ports speed. Depending on your exact model you could have a SATA II (3.0 Gb/s) or a SATA III (6.0 Gb/s) interface. Review the links above for reference.

While more expensive you might want to make the jump to a SSD! As an example a Samsung 850 EVO 2.0 TB. Note the spec sheet lists SATA II unlike the HD drive. This is the difference between a FIXED Vs AUTO Sense drive. Review what ever drive you get to make sure it supports SATA II if your system is SATA II.