It may be caulked out of sight, under the window unit. If not, as was the case for a neighbor, it could be the source of a lot of water inside the walls.
I would caulk it.

Brick veneer is similar to stucco where the underlayment/flashings is what keeps the wall dry. By caulking the bottom, you are plugging a drainage plane that allows moisture that has built up behind but over the underlayment/flashings the capability to run out and down the exterior of the brick. You do want to caulk the vertical,(each side of the window), as well as the horizontal over the top as a cosmetic insurance that water wont run in from the exterior from rains, thawing, moisture build up, etc. If the area under the window is showing signs of leaking from the exterior, it's more than likely an improper install of the underlayment/flashing method during the window install.

Would that mortite caulk rope stuff work ok in that application? It seems like mortite would be much easier to remove versus latex caulk if a window needs to be replaced at a some point.

IMO it doesn't seal as well thus the easier removal.

best of luck.

That is NOT a good place to seal.

It is intended to allow drainage as mentioned above.

I have a brick veneer exterior on front of home. Had a leak in bedroom beginning of March after a driving rain. Observed the window caulking around that window to have many gap/splits. See pictures at:
http://photobucket.com/outwindow

In mid March when weather was decent here in ohio I spent two hours getting all old caulk off window frame and brick and caulked new along sides top and bottom. I do not have pictures of the new caulk job but all joints are sealed now. April 4 we had a driving rain again and again water leaked but not as much as in March. After reading the post, are you saying I should not of caulked along the upper seam at the bottom of the window as pointed out with the red and yellow markings in the picture?

Thanks