That mobo has SATA 3.0 Gb/s ports, so it certainly can handle any SATA HDD unit in any size now available commercially. Since you do NOT plan to BOOT from this 4 TB unit, the limit VERY likely is in your OS.
The only way to use all of the space on a HDD over 2 TB is if it is Partitioned using the newer GPT system, not the old MBR system. Then you must deal with this: using a HDD done in the GPT system requires a different device driver in your OS than the older system. Within the Windows OS family, Microsoft does NOT include a driver for any GPT-type HDD in any of the 32-bit versions of Windows. The required driver IS included in all its 64-bit versions. So, to access anything on a HDD using a GPT Partitioning scheme you MUST be using a 64-bit version of Windows. Then, once that is running, you just need to install in it (like any other device driver) the driver for a GPT HDD.
Thus, if your Windows already running on this machine is a 32-bit version, you're going to have to switch to a 64-bit version. I'm not sure whether there is a simple upgrade path for that, or whether a fresh Install would be needed. BUT if your Windows already is a 64-bit version, there should be no trouble at all. Just be SURE that, when you Initialize the new HDD as you install it, you choose to do it using the GPT Partitioning system.