Yes, on the left hand side there is a mask icon (third symbol down) in the Compositor window to create a specific "box" shape.  You can then put a black gradient behind this on the next video track. There is also the relatively fast boxblur plugin that is very simple to use.  Just drag it to the video timeline, make the box the size you want, and blur it as much as possible.  It will not be black necessarily though.  If it is a moving item, you can enable "generate keyframes while tweaking" and put the box in different places as you move along.  Be sure to turn off "drag" before rendering (if you Mask or whatever) or the lines/points will be drawn too.

Also, there is the f_delogo plugin which blurs out a specific spot that does not move.  This is the ffmpeg included plugin.