You can see the operating system validated for the Intel NUCs at:
The Intel® NUC has not been validated to work as a server system as you would like to do it, so we cannot guarantee that this will work for you.
At this point I will recommend waiting for somebody else to share their experience with you and see if someone else made it work as you would like to do it.
Just my (pseudo-random) thoughts on this...
There are two issues, (1) how to connect 4 drives to the NUC that can be put into a single RAID array and (2) what software to use to implement the NAS functionality.
The NUC has a single SATA port plus either an M.2 (in newer NUCs) or mPCIe (in older NUCs) interface. In a quick internet search, I found only 2-port SATA cards in the M.2/mPCIe F/F. Some supported RAID, some didn't, but this is isolated to the two drives connected to the individual card (i.e. cannot use two of these cards to get a 4-drive RAID capability - even if you had a way to use two cards). What this means is using the SATA port for this capability. This means finding a RAID controller that can have 4 drives connected to it (in some RAID configuration) and this controller connects to the NUC via the single SATA port and it makes this RAID array look like a single big drive to the NUC. I have seen eSATA boxes that could be used to accomplish this (just configure the NUC's SATA port for removable devices), but I have never seen a standalone card with one SATA port on one side, 4 SATA ports on the other and some sort of RAID controller in-between. Obviously, the latter is what is required if you want to use this 1U chassis.
Presuming that you solve the H/W connection problem, next comes software. In the Windows arena, Windows Server and Windows Home Server are not supported. You could use standard Windows (7, 8.1 or 10) but my understanding is that the Windows networking interface is detuned for server-like access. You may need someone with the smarts to tweak this interface to fix this. The alternative is to use something like FreeNAS or some other Linux derivative. The possible problem here is support for the entity that provides the 4-drive RAID capability. If this is a H/W RAID solution, great. If it is a S/W RAID solution, you need drivers for it in the hosting O/S...
One more thought - there are plenty of mITX motherboards out there that already have the 4 SATA ports necessary. Many of these even have soldered-down Atom/Celeron processors. This may be the less complicated path to take -- though, getting RAID support may require that you go with at least a Core i3 solution (I am thinking of using something like Intel RST, for example; it isn't supported on the Atom/Celeron solutions)...