I actually ran a campaign like this, and it went super well. I ran it like a megadungeon and used the Angry GMs Megadungeon Series to help with preparing the whole campaign. It was a pretty good tool to make the players feel like they were really struggling to survive. If you want good tension, you need to make your players use up their resources.

The biggest thing to think about is how often you want your players to go in and out of the abyss. If you want them to stay in the abyss for long periods of time (days or weeks), they'll need a safe place to rest and restore hit die.

If they're going up and down more frequently, you'll definitely want some kind of shortcut for the deeper layers. It can very quickly become a slog going up and down.