Can this iMac support 4TB Hard drive?

There is no differences between this HD because of its size Vs any other from the hardware or OS perspective. The only thing you do need to look at is the drive is rated for single use as the builtin cache could be on the small side which you don't want.

But you will encounter issues as this series needs a custom HD that has a built-in thermal sensor. Luckily, OWC has created a special cable to offset this issue: OWC In-line Digital Thermal Sensor for iMac 2011 Hard Drive Upgrade which you will need.

The second issue here is heat! Bigger HD drives create more heat. To lessen the effect I would strongly recommend adding a SSD as your boot drive. You don't need a large drive here but you do need one that can hold your OS & Apps and still leave about 1/3 of the drive free for caching. By using a SSD as your boot drive all of the heavy I/O will take place on it lessening the HD's usage . While your HD will host all of your data files.

Here is the IFIXIT guides to review:

• iMac Intel 27" EMC 2429 Hard Drive Replacement
• Installing iMac Intel 27" EMC 2429 Dual Hard Drive Kit

As an alternative solution you may want to look at a Thunderbolt external RAID'ed HD system. Here you can get into some very large storage solutions and it can be faster than the built-in SATA III (6.0 Gb/s) drives. A RAID drive set can push the limit of your Thunderbolt port (10 Gb/s). In addition it is more portable in case your system encounters a problem.

So if you are planing on creating vids or music files you may find getting an external drive a better solution. I would also look at your systems RAM as you may need to upgrade it as well.