It is entirely possible to construct a 6 inch hole in brickwork. The problem with a round hole rather than a square hole is where the hole cuts across joints in the masonry leaving small triangular pieces of masonry over the hole. These tend to be fairly week so are best avoided. You would therefore have to position the circular hole carefully so that is best placed not to leave small or week sections of masonry. As mentioned in other answers to get a good hole, a diamond or similar circular hole saw is the best way but at this diameter you made need a large pillar drill rig to use the hole saw and this may need to be bolted to the wall prior to making the cut.
If you can fill it a square hole then may be better. Given the diameter of the hole you are suggesting you shouldn't have any structural problems as long as you aren't right next to openings or corners in the wall. The key is to make sure that the hole doesn't leave a whole brick unsupported from below when you make the hole and with a 6" diameter this shouldn't be a problem unless your bricks are very small. The neatest way of doing this is to cut out the edges of your hole with something like a disk cutter and then use an impact hammer to chisel out the brickwork in the centre. This should leave a very neat cut.