Add noise to video while maintaining compressibility
As you say, noise by definition doesn't compress well. You can try different types of noise in FCP. The Add Noise filter has several choices - Gaussian is a reasonable simulation of film grain, but you can try the other choices, too. They might compress better (or worse). 

But your best bet is to increase the data rate of the resulting file. I don't know the limitations of YouTube or Vimeo, and your content may make it difficult to stay within their limits, but that's probably going to get you better results than trying to find some form of noise that isn't (as) affected by compression.