the aldmeri dominion can't take black marsh, at least not by any means we know at this moment, the argonians are in their home turf, they have every advantage.
1) they are in their homeland, they know the land better than anyone else.
2) said land is full of diseases and argonians are inmune to many of them if not all.
3) said land is also a swamp, swamps are a very difficult terrain to move trough, so forget about steady supply lines.
4) argonians being what they are. are perfectly adapted to the swamp being able to breathe underwater as well as being superb swimers.
5) the hist and it's many vitues, sap, hive-mind, etc.
even if the AD wanted to burn a path trought the swamp, and im not even sure they could, they will suffer an incredible amount of casualties, you can smear arrow points whit all kind of stuff that would make a scratch become infected and put a soldier on his back or even kill said soldier.