Yes, it will work fine
The two types of 3.5" HDD are ATA (sometimes erroneously called "IDE") and SATA.
-- All PPC
iMacs use ATA.
-- All Intel iMacs use SATA.
-- All 2TB HDDs are SATA.
In general, HDDs that are at the top limit of current size technology are not as reliable as ones that are a bit smaller, so a 2TB size HDD in 2011 is not the most reliable. In tests of various HDDs, the results show that 320 GB and 500 GB HDDs are very reliable, but 1.5 TB and 2 TB sizes are less reliable.
You should also consider the wisdom of going to all this trouble if you don't have a backup. It makes more sense to buy a 1 TB HDD and a case to use as an external Time Machine backup. Then you have 1.32 TB of space.
Also, most of those "Green" drives are simply slow drives. They are 5400 RPM and that slow motor is how they save electricity. I suggest a 7200 RPM HDD if you want fast response... also a case with Firewire 800 for very fast copying. USB is dreadfully slow, no matter what PC geeks say. They don't have Firewire to compare, because most PCs are cheaply made.