the system requeriments can be found here: Supported Graphics Drivers on Linux | Unreal Engine Documentation
i would say yes, it should work but i’m not sure if intel HD have dx11 support, i would recommend you to buy a graphics card, my PC runs ue4 with a FX 6300 8gb Ram and a R9 270, it’s not perfect, it takes a lot of time to build lighting or packaging the project but at least i can use the rest of unreal without greater problems.
the point is, what kind of game you want to develop? i would say the computer to develop the game should be a little bit better than the one you would need to play the game, you won’t be able to develop a game with good graphics if your PC don’t have a graphics card or a CPU to play it. if you just want to develop mobile games or simpler games so buy at least a RX 460/RX 470/GTX 1050ti, you can buy an i5 instead of the i7 if you need to save money to the graphics card.
the requeriments you mentioned (32GB gtx 770 and etc.) is in case you want to build a really powerfull machine for your company to develop a triple A, and it’s far beyond the minimum requeriments.
unreal usually uses something near 1GB - 3GB of ram from my computer, if i sum with the rest of the system it sometimes get’s near to 6GB or 7GB, 16GB will be enough.