Yes, I maintain several GitHub repos. Almost all of them are, in a sense, actively open to pull requests.
My take?
Random pull requests are fine, especially for minor tweaks and small bug fixes. Even better, if the pull request fixes a known, open bug from our Bugzilla instance. In that case, it would be good to mention the bug #. We don't have a formal style guide, but unless the code is just hideous, I probably wouldn't reject a pull request on stylistic grounds alone.
OTOH, if you come along and implement a major feature with no interaction with the existing team, things might get a little more complicated. In those case, it probably is better to establish some dialogue first, just to make sure everything fits. Likewise for fixing a major bug with lots of interactions / dependencies throughout the code base.. assuming your patch really does fix it, then yes, we'd take the pull request. But it would be good to talk through it first, walk through possible "unintended consequences," etc.
And, of course, emailing or establishing contact first is pretty much never a bad thing. Well, as long as one follows through with what they say they're going to do.