The title begs the question, why would I want to do that? There are two philosophies about this that go back to the hardware world.
If you are recording singers and instrumentalists through compressors or reverbs, at that point it is a non-removable part of your audio files. Is that a good thing or a bad thing? Depends on the circumstances and your point of view. Obviously, if you are recording multiple parts and simply do not have enough of the desired hardware, you may have to do this. Back in their early days, The Beatles recording consoles and tape machines were limited and so they recorded virtually everything through a compressor, usually an Altec or a Fairchild, and I think it is fair to say that history has already decided that the result was pretty good.
That said, I used to work with two engineers with very different philosophies. Engineer number one used to say to me, 'I know very well what the sound is like recording through my specific compressor and I not only am willing to live with the resulting sound, I WANT that sound.'