Will this PC run Unreal Engine 4 well? (US$4000)

Honestly this build is overkill if you are just getting into developing with UE4, but I am not going to tell you not to take what’s being offered to you!

Watch out for the Noctua and the RAM height. If the RAM height is going to be a problem get yourself an AIO cooler.

As far as the Titan Black. in your case, I don’t believe it’s worth the price. You might think about the 780ti instead and using the leftover from the Titan to go with much better dual monitors than the tri configuration you have picked.