I don't know about the mumak list being competetive, but Harad is certainly competetive. In small armies (500 points or less) the mumak isn't the best idea but at around 750+ you could use him without problem I think.
Quick 750 point list:
Suladân, the Serpent Lord with Bow
2x Haradrim Chieftain with Spear and Bow
Mûmakil of Harad
2x Haradrim Warrior with Banner
24x Haradrim Warrior with Spear
12x Haradrim Warrior with Bow
That's 748pt 42men 15bows.
I think that's a pretty sollid list. You would need to buy a mumak, suladan, 2command blisters and 2boxes of Harad Warriors.
Hope it helped, and if you any questions ask them
Note: this is for SBG, if you want to play
WoTR than I can sadly enough not help you :(
Note2: the mumakil comes with 12 Haradrim Warriors, but that is not enough for this list so you will need 2 more boxes of Harad Warriors. In a box there are 12 of each (spear and bow) but in SBG there is a bow limit of 33% of you army (without heroes)