Oh, it stands a chance of invading. A very good chance. It's trying to invade my hugels, but I pull it regularly.
You're not going to keep it out with flashing. If you dig down 24", some little bit of stolon will be down 25" and will find a way to make it in. Metals rust, plastic cracks, and each little hole or fissure is a new place that the bermuda grass stolons
will find. The only way you are going to keep it under control is by regular culling during the growing season. If you are in a place with freezing winter weather, it goes dormant for those months, and you can get well ahead of it.
Permaculture is a process of applying constant pressure to nature to bend it toward our needs. Part of that constant pressure is to selectively remove plants that are too exuberant (commonly know as 'weeding') in addition to applying TLC to plants that have a little difficulty getting started. One positive about the weeding of a hugelbed is that the soil around all that buried biomass is so loose that the bermuda grass comes right out in one pull. Quite different from trying to clear a patch of compacted high-clay soil where you yank 3" of stolon and the other 18" stays in the ground to sprout again.