I think they can as ants need water and maybe taking it from your lawn. If you have pets or children using your lawn get something that uses diamatecious earth. It is non-toxic and will kill the ants. There is also EcoSmart bug spray, which has been working well in my house. I don't know how plants will react to it thought.
It sounds like your lawn is destroyed all ready, they can be a real pain to get rid of, & it'll take a while.You can call local exterminators, they'll more than likely use poison, many folks today frown at poisoning anything-that's your choice You can use other means: place 1 quarter to a half oz.of eucalyptus oil into a plastic spray bottle, fill it with water & go to town.You can use vinegar, or boiling water, dig a small hole into the anthill pour the boiling water inside, ditto with the vinegar Boric acid works-anything to kill the queen, you can leave bait stations