Will verbana bracteata overtake grass?

I live in eastern North Dakota, in the Red River Valley, and found some verbana growing in my backyard.

I'm doing some landscaping of this corner plot of the boulevard (I know, gray area, but law enforcement neighbor doesn't expect a problem to come of it and says to be emotionally prepared for its destruction if necessary).

Anyway, what I want to know is if this verbana will naturally overtake the grass?

I have planted a hosta (eventually more, just haven't procured more yet) and a bit of viola from my flowerbed, plus some transplanted verbana. I don't want to till or remove sod–just keep it low effort.

So am I wasting my time transplanting or could this possibly work? I've discovered about 10 more easily movable bits of verbana in the back.