Rationally landlords should not care about pet ants because they won't scratch things or leave hair around which is what landlords worry about with cats and dogs. (And they worry too much.)
The laws are probably on your side so I would just not ask.
Often the law doesn't even allow "no dogs or cats" rules, but this varies.
Landlords can be upset about damage if it occurs and that's about it.
Irrationally? People think ants will "spread" this is so impossible it's absurd.
futurebird