Good question. HD yes; but 4 K??? Please post if you find out.
Mac Pro, macbook pro, Imacs (i7); Canon 5D Mark III/70D, Panasonic AG-HPX170/AG-HPX250P, Canon HV40, Sony Z7U/VX2000/PD170; FCP 6 certified; FCP X write professionally for a variety of media; teach video production in L.A.
I've edited some basic 4k stuff on an 11" MacBook Air so I'd assume you could get away with it on that spec iMac. It probably won't be the most fun you've ever had but it'll probably work. Using proxies will help a lot.