Is Black Locust invasive?

The short answer is "Yes, Black Locust is invasive."

The nuanced answer is that Black Locust's invasiveness can be a benefit, neutral or very undesirable depending on the situation.

Undesirable
In a lawn, in an orchard or vineyard or garden. Almost all Black Locust are thorny with the thorns varying from modest to ferocious. Suckers pop up where roots run close to the surface. Cutting the suckers causes two or three more to pop up.

Neutral
As a companion or nurse tree where the other species is a fast grower that ultimately grows taller than the Black Locust and overtops it. Black Locust rarely gets more than 45 feet tall around here.

And example would be a pollard planting where every third tree is a Northern Red Oak or perhaps a Bald Cypress.

Desirable
You have crappy soil and it is difficult to plant due to rocks or slope or you are just too darned busy. Those root suckers will fill in the spots you can't get to.

Regarding the thorns: They tame down a bit as the trees mature. The thorns are most fierce when the trees are juvenile which makes sense as they are there to repel browsing animals. Also, quite a bit of variation from selection-to-selection. Black Locust seed is cheap. Much of it comes from Hungary where they have been selecting for good tree form and low thorn size and count.

Pour the seed into boiling water that has been taken off the stove, stir for two minutes, drain and wash with cold water.

Scatter thickly. Grow for a year and keep only the most thorn-free.