Above treeline i see this being ok in calm to fair weather, but turning into a possible disaster in a storm or with strong winds. There would not be enough structural support for the shelter. It would be like a ships sail in the wind. I am sure it would work great in a more sheltered location, so site selection would be key.
I use a Warbonnet superfly tarp year round with my hammock and understand a tarps limitations, and have even taken my setup to -30F and weather some severe storms. The ability to tie off to trees or rocks should not be underestimated, it plays a vital role in the structural integridy.
The main issue i see here is without a solid center pole providing taught tension the shelter would be highly prone to collapse. The three pole idea is a good one, but without some sort of sleeve etc to run the pole in would actually make the shelter fairly weak. A tripod does not do well at all with crossdirection pressure. If your pushing against a pole, or direct from the top it works fine. But push between poles and it will have a high probability of collapse with nothing else supporting the pole/holding in in place.
If you want to go with a pyramid setup i would either 1) use a center pole and just use a slightly bigger tarp for more room, or 2) camp below treeline.
There are many good ways to rig a tarp with trekking poles. These methods would work much better than trying to rig up something with extra poles.
Check out this video, the first two setups shown are what I would recommend. The first would be kinda what your aiming for...i think, and is very strong.
http://www.youtube.com/watch?v=9SGFUXpzPGQ
Not trying to be a grouch, just speaking from real world experience.
