You'd have to define deep I suppose. I think it probably IS fair to say that most fossil seabeds were not from what we'd call the Hadal zone nowadays.

Hmm. Actually, they have a pretty good idea of which plates were where at different epochs and I'm not sure there IS an exposed rock face that would have been Hadal, and I'm not sure that geologic processes are particularly likely to result in present trench communities to fossilize and then be exposed some time in the future. My general impression of most of the truly deep sites is that they're rifts at the bottom of subduction zones and rock that ends up sinking below a plate isn't coming out looking like it did when it went in. I THINK. I study evolution but not paleontology or geology. If someone does know of one I'd love to read about it!

You might find this interesting:

https://www.jstor.org/stable/20144263

That's a paper on a fossil anglerfish. Not all anglerfish live in the deepest parts of the ocean, but apparently they think the formation that one is from represents mostly fish from around 1000m. It certainly gets deeper than that but a lot of what you'd see living there would be "weird" compares to the fish most people are familiar with.