Only if the client has access to the full bit depth. The rendered PNGs are uint8, but the underlying raw data is often stored in 16 or even 32 bit precision.

I imagine that with HTTP range requests, it shouldn't be hard to access original TIFF data. Javascript or WebAssembly can then work with arbitrary bytevectors.

Yes, it’s possible. There are some proofs of concept for that IIRC. If you prefer to write everything in Javascript you can do that and do all heavy lifting in the client (plus some extra work to provide indexing and metadata like Terracotta).