Wow, I wrote a lot more than I was planning on. So here's the tl;dr version:
It would be simpler to upgrade the entire system to Maverick than backport Evince 2.32.x to Lucid.
Is it safe?
First we need to address the question of whether this is safe. In most instances, installing new versions of so-called "leaf" packages will not effect the stability of your system. A "leaf" package is a package that provides a standalone application that no other packages depend on. Evince, unfortunately for your purposes, is not entirely a simple "leaf" package.
Evince 2.30.x also provides the libraries libevdocument2 and libevview2. While Evince 2.32.x provides libevdocument3 and libevview3. Notice the libraries' have different numbers. This shows that there has been a SONAME bump meaning that there have been incompatible changes to the ABIs of these libraries. Other programs that rely on libevdocument2 and libevview2 may not function with libevdocument3 and libevview3.
Fortunately, at least on my system, there are no other programs that rely on libevdocument2 and libevview2 besides Evince itself. So is it safe? Probably!
Is ppa:irie/evince safe?
As with any other PPA, this question comes down to whether or not you trust the owner of the PPA, in this case irie. There are a few ways that I use to determine whether I trust a PPA like looking at the breadth of their contributions. Are they also a upstream developer? Are they an Ubuntu developer? Does their Launchpad page show on going activity?
As for this specific PPA, it seems to introduce change that are not yet upstream:
This PPA provides slightly enhanced
Evince document viewer that pan scroll
mode (like "Hand tool" in Adobe
Reader) is added. It's probably
suitable for touch panel based
computers. The code changes are based
on a patch written by Stephen Sugden.
But more importantly, it doesn't seem to have packages for Lucid. So it will not help you anyways.
Backporting it on your own
So since its safe, is it doable? It depends on just how much you want it. Unfortunately, it would take quite a bit of work to backport Evince 2.32.x to Lucid. Backporting a singe package isn't that much work, but looking at the source code I can see that it's not just Evince that needs backporting. It needs newer versions of libglib2.0-dev, libgtk2.0-dev, libpoppler-glib-dev, and libcairo2-dev that are not available in Lucid. Those are core GNOME libraries that are about the complete opposite of "leaf" packages. You would need to backport the entire chain of dependencies.
In short, doing so is very complicated , time consuming, and potentially dangerous.