This is certainly doable, and understandable. But also challenging.
My idea for a short 10-day DG safari is to prepare in advance all I can prepare to my advantage to cover all shooting conditions and scenarios, knowing there will be enough of variables once I get to African hunting grounds.
With scope I had: 3 accurate shots on buffalo (100 meters, minus few steps while approaching between shots), elephant brain shot, 100 meters, and 100% success rate on plains game up to 200 mtrs. No game lost.
Shooting iron sights for all that would make a totally different hunting scenarios, with possible different success rate.
Shooting iron sights with double, will require to approach close, no longish shots to be taken, and shooting in the bush will be difficult, with aiming to pass the bullet properly between branches, leaves and under a shadow, to that smallish dark spot of vital area.
It is of course doable, but also challenging.
To illustrate my philosophy, this is the scenario that I try 'to avoid at all cost (start at 04' 30''), 40 something meters distance.
Then listen to lesson learnt (at 08' 36''):