I would leave it. Anything that protects the vulnerable bits like oil pan, and in your case drivetrain, from road debris is worth having.

Just search the internet ... there are plenty of photos of ruined engines.

Just to make sure I follow, you are referring to the underbody panels between the engine and the ground, not the "beauty cover"over the engine underneath the hood?

Those panels keep the engine cleaner, reduce noise and improve fuel efficiency.  But they aren't necessary, strictly speaking.  If you want to take them off, go ahead.  But don't throw them away in case the noise is too much or the car becomes unstable at highway speeds (like if the nose starts to lift a little bit).

Mine fell out in the road ages ago, hasn't caused any problems.

If you do a lot of highway driving, I’d leave it on because it’s supposed to aid with fuel efficiency because of aerodynamics (smooth airflow).

If your usage is only within the city, on good roads and at slow speeds, then go ahead and feel free to remove it.

But like @mmj said, it helps avoid underbody hits & road debris enter into the engine compartment.