Oh yes. you should put in the black space to let the eye rest before it takes in the abstract squares border. I love the design and the fabrics you've chosen. Your project is going to be delicious when it's finished.
A hint for speeding up the patchwork process on the log cabin blocks: Sew all of the center square to the first side, chain stitching all of your blocks. Go to the iron and press them towards the strip you just added. Add strip two to all of them. Press. Strip three, press . . . this way you will get them all going in the same direction (clockwise) and finish much faster.