That unit certainly can use SATA 6.0 Gb/s HDD units.
Use of HDD units over 2 TB each very likely is OK also. The manual for it says it can use HDD's up to 3 TB, and the web page quoting specs for it claims up to 4 TB units are OK. Now, the issue involved is in a detail about the type of "LBA Support" used in the system. There are only two types officially, but Microsoft sort of imposed a third sub-variant in its 32-bit operating systems and the MBR Partition system.
In the context of internal HDD's in a computer, the original LBA system for addressing Sectors (or Allocation Units) on a HDD used 28-bit addressing. 28 bits is sufficient to address up to 128 GiB of data (one GiB is 1024 x 1024 x 1024 = 1,073,741,824 bytes). The newer 48-bit LBA system can address vastly more that that, so for any practical purpose that is no longer a limit at all on the size of HDD's you can use. However, 32-bit versions of Windows until recently used a 32-bit LBA sub-variant, and that is what has limited HDD use in some machines to just barely over 2 TB. Closely linked to that is the system for Partitioning a HDD. The older MBR system used a Partition Table with entries for the location (read, address) of the start and end of each Partition stored as 32-bit numbers, so any HDD Partitioned in that way could only use 2 TB of its space. The new GPT system, among its many changes, uses 48-bit addressing in the Partition Table to avoid this issue.
In order to be able to use HDD's over 2 TB, your system needs to have 48-bit LBA Support on three components: the HDD itself (obviously will for a large HDD), the HDD controller, and the Operating System that calls for disk access.
The Akitio Hydra Super-S LCM enclosure clearly says it will use 3 and 4 TB HDD units fully. (In fact, in case someone has a very old OS that cannot deal with large HDD systems it has an option to limit what it does.) Thus it must be using 48-bit LBA.
Last item is the OS and its device drivers. For a Windows system using only internal drives, there is another consideration related to Partitioning. Only HDD's partitioned using the newer GPT system can access over 2 TB. Thus Windows needs to have a device driver that works with such drives. But Microsoft has only included a driver for GPT-Partitioned HDD's with its 64-bit versions of Windows, and not with 32-bit versions. Your situation, however, is different. I am sure your Akitio enclosure came with a driver for it so that Windows can use the enclosure and whatever RAID array you created with it. I would expect that that driver can handle any size of RAID5 array built with any HDD available. I also expect that the driver can work with either 32-bit or 64-bit versions of Windows. Otherwise it could not have worked with four 1 TB units that give you a RAID "drive" over 2 TB total space. HOWEVER, you really should ask Akitio about that to be sure.