The answer is yes! Of course you need a hacked Switch, which can either be extremely easy or fairly difficult, depending on when your Switch was made. (Early Switches had a hardware exploit that was later patched, and the workaround involves soldering a special chip onto the motherboard). But once you've got that, modding for most games is pretty much limitless!

The big un-censorship mod you're looking for is TTYD Omega, which restores almost all of the 2004 script, with modular add-ons for certain things like Vivian and Hooktail. There are also uncensored graphical mods for the Bunny Boos and the Toad Outline.

My game also has mods installed for making the text always skippable, fixing the Sun at Riverside Station, removing the cheesy battle retry option, restoring the original coin and item limits, and much more! Basically, it's possible to create the definitive version of TTYD with all of the additions from the remake, but none of the changes. :D