It's a good idea to cover it. I had initially had DH cut the board to cover it as we had an old dog that was attracted to the steps like metal to a magnet.
He is gone now, and I had stopped using it, but keep it behind the one seat. Last year when we had the GS along on a trip, he woke us up in the middle of the night with a blood curdling scream.... by the time I got out there (he sleeps on the sofa) he was at the door trying to get out. He wasn't really awake. I had a dog gate propped across there that night, and that's all that kept him from falling down the steps.
Then last fall, on a trip, at 3 am a car alarm went off. I got up to see what was going on and I actually missed my footing and fell down in that step-well. Ouch!
Since then, I put the board down at night. Lesson learned.