Is falling through trap doors worthwhile?
Yes, falling into trap doors leads to many treasures.
You should still always consider saving first, after that just jump into every trapdoor you can find and enjoy the bonus loot.
There are several "hidden" areas that can only be accessed by falling through holes.
So I would actually try falling though all the holes (you can usually check once below which holes lead to new areas as the a hole 2 block to the right, will drop you down on the level to blocks to the right).