Is LinkedIn often used as a resume? LinkedIn to me is a social media platform. At least in the software companies I've worked for, and applied to, I've only ever seen actual resumes around.
Effective communication is absolutely something I'm looking for in a candidate. The ability to communicate clearly and succinctly in writing is critical. I've worked with far too many people who'll respond to a question with paragraphs of narrative and reasoning and background information without actually giving a clear answer to the question.
There's a really tiny niche case where someone might notice or, if you point it out, be impressed or amused and have some say in the hiring process, but these will be weird rare situations that you can't predict anyway. I think you should do your resume with your most comfortable tool, and that might be LaTeX (in which case you can expand on it) or it might be Google docs and you know what? That's a pretty common documentation skill to want to have, too.
I don't have a LinkedIn, and it doesn't let me view a profile without an account, which forces me to pass on applications that don't have a CV attached.