No.
So that's why you have to be careful, I've found they'll display the full 720x576 which means if you've capture from say VHS and have ragged edges they'll be visible which is why I always mask them out.
Actually, as I understand it, they DO actually have a certain degree of overscan, however, it's far less than with current analog sets. The number I've heard is 2%, but I could be wrong.
I suppose that it makes sense-- if it wasn't overscanned, we'd be able to see the captioning line, etc.
I've had exactly that problem with Digibetacam. We couldn't find a way to turn off the embedded TC, in I think it's line 21 and when that was down converted to DV that I was burning to DVD it was easily visible on LCD screens so I had to mask it out in Vegas.