Yes it is possible to dynamically skid a turn without using torsional flex. It is a bit inefficient and funky, but possible. In essence, is could be done by tilting the board on edge (using both feel like in carving) and then forcefully breaking the edge hold by deliberately pushing the board to the outside of the turn. new riders who kick the tail around do this. Sadly, they think it is good riding, when in reality it is poor form...but it does work. Use of torsional flex in dynamic skidded turns is very effective and makes the entire turn easier and stronger.
I don't kick the tail around, I'd say I've done the dynamic skidded turns without flexing the board but then again when I'm riding I don't really think about my legs at all.