No it definitely does not. The stage that is dropped is guaranteed to hit the ground before the lander. That's simple physics. The top continues to slow its descent while the bottom portion accelerates under lunar gravity towards the ground.

There's not much concern about it landing in the landing zone either. There's nothing to move the dropped stage off course. It's a simple ballistic trajectory. They'll plan a path, drop the stage so it follows that path, then continue their controlled descent which will use a different path to the surface.

This is exactly how nasa does it with landing on Mars. The heat shield is jettisoned and allowed to fall to the surface. It's done in a way that will keep it out of the final trajectory, and landing site, of the rover. There's no risk of it landing on top of the rover either, since the rover has a slower descent.

The main risk with the propulsion stage over a heat shield jettison is that the propulsion stage will still have residual fuel. Their main concern will be making sure it can't send debris flying over vast distances that could cause problems for either the lander or existing infrastructure.

If we get to the point of planning around existing infrastructure then it will likely mean they will have a set landing area. Stages dropped off will likely aim toward a "debris field" where they drop them towards an area far away and not planned for human visitation. Then the landers will land in the landing zone. Where they also will then take off from clearing the way for additional landers.

Plus now the ascent stage has to use its engine twice unless I'm missing something. I'm really not seeing the benefit compared to Apollo-style.