In the manual, it read that the batteries in the VMU would last 7 days of continuous gameplay. Which translates into about 168 hours, if that is what they meant. This also means that, yes, playing games drains the batteries. My VMU batteries have lasted for ages now, it feels. I\'ve only racked up some 100 hours of gameplay on my DC, though.
And of course, if you don\'t want to waste good batteries, you could always take \'em out of the VMU. Even without them, it should still work as a memory card (at least I remember reading so from the manual).