No guarantee on 4.4 it will depend on how much voltage the chip your receive needs to be 100% stable. By the way that is a very good choice going with a Cryorig cooler I replaced my H100 water cooler with a R1 and actually lowered my temps a couple C.
If your in for the long hall and the H5 will fit in your case I would consider the extra 15 bucks or so a fairly good investment for when you need to overclock the processor a bit more when it's near the end of it's performance life. That might buy you another year before rebuilding or buying a better cooler.
You should be able to get 4.4 in the 1.18/1.19 area (depending on the chip) on the Vcore voltage, my 4790K at 4.6 is on 1.22