This type of fancy cakes usually has inedible internal supports, such as wood rods. I wouldn't trust the cookies to remain safely upright even after being glued. My intuition would pronounce a glued tower stable if its height is 2x diameter max, anything above feels problematic. It is a different case if you create a hard tower with the cookies somehow embedded in it, but this means we are talking something like embedding cookies in hard candy, which doesn't sound appetizing and probably looks strange. In the end, it will probably work better without cookies.
The alternative would be to create maybe a four corner "basket" out of rods to put the stack inside, and decorate the stocks nicely. In this case, you can use a fairly weak glue, even some whipped cream will be OK, because the glue doesn't have to support the structure.
There are videos on the Internet for creating fancy cakes, often episodes of reality TV shows. You might want to watch them for inspiration. I haven't seen any with a cookie tower, but I have seen 3-D models of stag heads and other sculptures, you can learn a lot from them.