Yes it does, which is my favorite part - although I don't get more than a few drops leaking.
I like to use a test jar for my sample for several reasons - most notably that I can put it down - and having that valve at the bottom makes it easy and mess-free to get the beer into it.
I don't have to hold onto the thief/autosiphon with one hand while taking the measurement (and dripping on the floor) with the other, which is convenient. I also find that I get a lot of foam in the top of the thief when I take a sample, which makes it hard to get an accurate reading. With a test jar, I can let it settle and take a hydro reading at my convenience.
Personal preference. Here's how I do it - click thru for HD if you like:
-Joe