What if the civ expanded their borders by giving a build order within their hidden capital for new sand sea tiles, just like building stuff in an ordinary city. Cities that get "devoured" by the sand sea give a production boost to the hidden capital, so the capital can expand cultural borders much more rapidly as it devours more cities. Devoured resources and mana nodes may also give specific bonuses, such as unlocking new units or abilities.
We may need to come up with a completely new research path (or a number of paths) specific to this civilization as well.
The hidden city could build a unit that sacrifices itself to add a new tile, or is that too boring? Maybe the Sand civ can't capture cities, it can only devour them. When at war the sand civ must eliminate a cities defense, then send in the special unit to devour the city. It could take one turn per population point so you can try to save your city before it is devoured. The special unit could also convert contiguous tiles that aren't claimed and when at war they can steal tiles from other civs.
I was wondering how the standard tech tree would apply to this civ. I think adding their own research path may be the right way to go if it doesn't make too big of a mess on the tech screen. Maybe it could be a tech like future tech that just keeps increasing in number. Instead of researching like normal they could spend certain devoured stuff on researching new techs in order to become more powerful and increase the combine limit of their units.
In fact, now that you mentioned devour, it makes me think that that could be the way this civ goes about obtaining just about everything. Everything it devours gives it "points" it can use to purchase new techs, units, etc... Anything that is converted to desert counts. Grass, trees, resources, cities, units that die in the dessert, mountains???...
Also, trading could add to this civ's "devour points" so they don't necessarily have to be at war or expanding all the time. They could come equiped with their own special resorces to trade to other civs' that become available as they advance on their tech tree.
Some bitter sweet things they could trade to other civs:
Greed: the civ's gold is increased by a certain percent but crime rate goes up a bit.
Glutony: the civ's food/growth is increased by a percentage but unhealthyness increases a bit.
Lust: happiness up, culture slightly down
Wrath:Less war weariness and more military production, slightly less general production
Envy: research higher on techs known by other civs, slightly slower on others
Pride: Higher wonder production, slightly slower growth rate
Sloth: culture up, production slightly down
Each one should be balanced so the good out weighs the bad. The seven deadly sins is just an idea, it could be changed to something else. Anything that is traded back to the sand civ would give it a certain amount of points each turn to spend on stuff.
I can kind of see the outline of a complete civilization now.