Your bog design is unusual. In all my reading about bogs I've never heard of anyone using either sand or underlayment in the construction. I will tell you our experience with using underlayment in a down flow bog. We built our rain exchange with several layers of underlayment between layers of gravel as we were told it would help with filtration and also keep the gravel from falling into the rain exchange. The latter is indeed true; the former is completely false. The underlayment very quickly clogged with fine sediment and prevented water from flowing through. We were cutting the underlayment out from under the gravel within the first few months of our pond being built. By year two we had to remove all the gravel and cut out all the underlayment. I don't recommend it. If you have water entering your bog that is filtered and free of all sediment you might be fine, but otherwise that underlayment is going to cause issues.
I would have the same concern with sand. People have experimented with using sand filled pool filters on ponds and find that they clog very quickly. Again, if your water is entering the bog completely free of all organic material, including fine sediment, you may not experience issues. I'm guessing the underlayment was suggested because of the use of sand. To me, the two either alone or together spell maintenance issues in the future. Just thinking out loud here - obviously I don't have any experience with this type of bog. I wonder if this was a design someone came up with for a swim pond, to mimic a sand filter in a pool?