Last year I set out to produce my master's thesis using only free software. Having turned in my final copy today, I can report a qualified success.
Despite some early interest in using Lyx (maybe someday in another life), I ended up going with a standard word processor in the form of OpenOffice (and its cousin NeoOffice). The downside in doing so is that I would have to deal directly with formatting issues. Thankfully OpenOffice has some versatile formatting styles which allowed me to satisfy the crazy formatting requirements (seriously - can I have a type-setting degree too?).
As for operating system, I was split between Gentoo Linux (free software) and Mac OS X (decidedly un-free software), where I did the majority of the actual typing. This is where the qualified yes comes in. It has nothing to do with any deficiency of Gentoo or OpenOffice. Rather I only had one machine available, and it had to be running Mac OS X for another reason, so it was just a matter of convenience. As it turned out, some font rendering problems in NeoOffice brought me back to Gentoo, which is the platform upon which I produced the final form of my thesis.
It all worked out in the end. So yes, it is possible to craft a big, important paper using free software tools.