They aren't really invasive, just not native. They are the least aggressive non-native ants I've come across. Very shy ants, any slight disturbance and they run and hide back in their colony. Rather harmless. Still not native though, and personally, don't care if someone digs up or/and kills non-native ants. People do it all the time to Solenopsis invicta and Argentine ants.
I'd think more harm comes from having non-native ants around, than actually native ants. I'd love to have tons of Pogonomyrmex, native Pheidole and all the native species of ants that are in California. Sadly, urban areas and ant introductions have lowered or gotten rid of native ants entirely in many areas.
But that kinda goes to the silly topic someone made on Antdude's forum about having non-native wildlife is better for the environment. Dunno what wacko would think that lol. I know this is about digging up ants, which I wouldn't agree doing with native ants. But, to me, non-native ants are fair game.