Should I learn to use LaTeX to write up a History Masters Thesis?
I'm finishing up a PhD in philosophy that I've written in LaTeX. Here's some suggestions:


make sure your advisor is ok with leaving you comments in pdf. I suspect he or she will not understand the question and will not be able to give you any feedback unless you submit chapters in word format. This is a deal breaker. Don't make any more problems communicating with your advisor than absolutely necessary.
lots of academic journals in the humanities still don't accept submissions in pdf or latex source form. If you are planning on submitting your stuff to a journal, you might save yourself time writing in word format.
there are some tools available to convert latex to rtf, html and other tools. texht is the best.
If you do decide to go LaTeX, don't get lost in the minutiae of learning how to tweak everything. It's easy to lose lots of time learning new packages and stuff when you should be writing, writing, writing. Use the wikibooks latex guide as your quick start guide when you need to learn how to do something fast.
Especially if you're on Ubuntu, don't get the LaTeX distributed through Canonical's repositories. It's usually out of date (haven't checked in a while). Just go on and get the vanilla TexLive 2013 distribution from CTAN.
The tex.SE site is really, really good. Like ridiculously helpful.
If you are familiar with version control programs like git, mercurial, or svn you can actually keep a very precise idea of exactly how your thesis has grown over time. You can roll back changes, etc. This is kind of advanced stuff for LaTeX, so I wouldn't spend like a lot of time learning this stuff if you aren't already familiar with it, but if you are, it can be really helpful. EDIT:  Per @henry's comment below, see the following guide by Roger Dudler to get started with git.