Since I wrote this question in '13, spurred on by the answers of Dave and user5785, I've become a hopeless alternate picking nerd and can give a definite answer here.
When people perform what is called "strict alternate picking", they're almost always synchronizing the right hand to the musical pulse--so if you're playing a run of eight notes, you play downstrokes on the 1, 2, 3, and 4, and upstrokes on the "and" beats in between.
If you have a rest, you play a "ghost" stroke to be ready to play the next note on a downstroke. Even players who specifically say "I alternate every note" are often actually doing this. This flavor of alternate picking might be the single most common way to play guitar, yet it doesn't have a name.
This rhythmic method automatically makes you accent the downbeats (you almost can't help it), plus the steady movement of your right hand helps keep you in time. As I recall Chris Thile advocates alternate picking to help you stay in time (though the video I originally linked has been taken down).
Many players, especially in the bluegrass world, take the "ghost stroke" thing to its natural extreme and keep their right hand bouncing all the time. This helps you feel the beat and make sure you're coming in with the right stroke after a rest.
A few players, mainly some jazz guys, recommend literally alternating every single note. The improvements I was feeling in my playing back in 2013 came from this constant hand movement, and I didn't notice because the phrases I was using to practice were mostly runs of eighth notes without any phrases that started on offbeats or other tricky scenarios.