Uuugh, we had a large one at our old residence, next door, and I pulled up hundreds of seedlings each year. They'll rapidly get away from you, too, if you miss them, they're very fast growing. We lived there 6 years, it was a mature tree, and I never spotted any suckers, so I'm not sure about that.
I'm a gardener in SW Minnesota, (the banana belt, LOL) zone 4B. I've been lurking here for a short time and enjoying all the beautiful pictures! I hope to share some photos of my own garden, too.