It would likely be difficult.
Unless they somehow tap into a bigger aquifer, Garama is going to dry up. However, a bit of luck, be it an earthquake cracking it open, or digging to it. Or the development of some sort of reliable dowsing technique.
However you could see their civilisation expand into other areas - such as coastal Libya - and its conflicts with Carthage could lead to N.African Garamentian cities. Another area would be the basin of Lake Chad. We are talking about people who lived and traded across the deserts. They could have various far flung settlements from W.Africa to Sudan, to Ammonium.
It may all splinter if Garama dries up - and form successor states of the civilisation - but they could be a great empire in their own right.
The problem being is that an Empire build around the Sahara is vastly different to one around the Med. It'd be built on the wealth of trade rather than the wealth of agriculture, which gave Rome a huge advantage over Carthage in terms of the level of manpower they could support.
If you want to go nuts, you COULD have them engulf the Sahara and the Med. That empire would be impressive, but so decentralised that it isn't worth calling it an empire.