Not sure the Romans would have the capability to do it fully. They could pierce through the Chott El-Fejaj easily, it's "just" 21km of a populous province, so with plenty of workforce. However, the Chott Jerid which comes after is 15 meters above sea level and would need to be pierced through to go to the el-Gharsa and the Alegrian Chotts (Melhrir and Felhrir).
http://terryking.us/photos/acst-maps/Topo-TunisieCarteRelief.jpg
Admittely, it is relative terms, out of the options, 21km is the smallest length to build a canal for any of close-to-sea projects
https://en.wikipedia.org/wiki/Chott_el_Fejej
The Chott Djerid (which I understand is the same), is 10-25m BELOW sea level, at least according to wikipedia.
https://en.wikipedia.org/wiki/Chott_el_Djerid
I think you're right, anything further than Melhrir and Felhrir is a nightmare as it is uphill. No point, no advantage there. However, these both lie almost entirely below sea level
https://en.wikipedia.org/wiki/Chott_Melrhir
However, interestingly for all these - that first 21km dig, is the longest - and is half of the digging work. Since all these Chotts are below sea level, it goes from an open series of salt flats that could be invaded across by any rebellious tribe to nearly 250km of watery protection, logistics, and potentially arable land.
Note found this image/map, the black bits, below sea level, covers a bit more than yours did.
http://en-gb.topographic-map.com/maps/9.052762312555299,-27.600911774999986,44.804854280851266,30.934244475000014/background/?Name=Algeria
Ad in the prevailing wind that goes south->north, then most of the rain would fall back into the Atlas Mts themselves, which (perhaps a foolish hope) could lead to the rain filling up the Tarf, or the Hodna, which could have all sorts of side effects. I'm particularly optimistic about the impact of extra water on the eastern coast - where there are other chotts that would have been filled by reborn rivers from the old wadis.
As a side note, as much as the prevailing wind is the other direction, I wonder if there would be a significant effect in the hills near Libya - if there was enough south easterly wind, then rain could get caught here.
The question is also why? Numidian were client kingdoms and I'm not sure it's worth the expense. Let's rather send a few legions there, right? However, maybe if the Numidians are more dangerous or if the Empire has an extended period of peace it could be done, maybe by a Senator trying to cultivate a power base in Tunisia.
The Numidians weren't entirely loyal (or at all by some arguments), and they weren't the only people there. The Gaetulian tribes were never (AFAIK) subdued. Certainly under Diocletian the Numidians as well were rebellious - and the Romans could only with surety claim control upto the edge of the mountains. It is much harder to deploy a force from mountain valley to mountain valley, than along a river/canal/waterway protecting a plain. So it could reduce the costs of protecting Africa - freeing up long term resources elsewhere.
Now, if the Numidians are largely peaceful, it could be done - as you said, by a Senator wanting a power base in the area. In fact, harsh as the work would be, it could be a fantastic project for penal labour. Punishing, beneficial to Rome, cheaper than hiring people or buying slaves to do the work, and as such doesn't need to be particularly rushed. Ideally though, you wouldn't want it do be done that way.
Anyway, I would think it could rather be done during the Third Republic, when it was studied and the project was approached by none other than Ferdinand de Lesseps
Whilst I think he'd do it better, with better technology and less loss of life, and quicker - I think the earlier the better, as it preserves the Greener Africa that was supposed to be there, and has longer to take effect. We may only see the major effects of his work by the 1950s.
