The simple answer is no! Coronal holes come in all shapes and sizes, and locations. Whilst they are mostly found covering the poles of the Sun, they also appear elsewhere. Their shape and size changes with time over weeks and months. They can be round or long and thin. Usually, they are irregularly shaped, following the outline of the open magnetic field region. In comparison to the Earth, coronal holes are huge. Of course, the Sun is huge, it is one hundred times the size of the Earth. Even a small coronal hole covers an area 100 times the entire surface of the Earth. The polar coronal holes can cover up to 10,000 times that area. You see, the Earth is quite small in astronomical terms!
Here is a really impressive picture from SOHO, well actually it's a bit of a cheat because it's two images, one from EIT (inside the dark ring) showing the hot corona and one from UVCS (outside the dark ring) showing the streamers. What I want you to notice is the dark coronal hole which stretches all the way down from the north pole past the equatorial region. This was called the elephant's trunk, can you see why? Even scientists like to have a joke or two sometimes.
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