Do I need to caulk around those little overhangs over my windows?

My house has siding -- part of the house has aluminum siding, and part vinyl. My windows have these weird little overhangs, which I assume are there to limit the amount of water that runs down the siding and along the window frame (btw, most of my windows are on the sides of my house that do not have eaves over them -- I have a high-pitch roof, with eaves on the two opposite sides).

When I started really looking at my house, a year after I first moved in, I realized that there had been some caulking around those overhangs. However, I was never sure if this was correct.

Should those things be left alone, should they be caulked, or should only parts be caulked? If only parts, then which parts?