If the stall warning was perceived as real, you would expect the nose down input to be sustained but with some puzzlement (to be solved later) as to what delayed the warning. If the warning was considered spurious then there is still no reason to pull back on receipt of the warning because it is, erm, spurious. I can't imagine a train of thought which would cause a pull back on receipt of the warning, purely because of the warning.
On the subject of the intial climb, really can't progress without the CVR can we ? If the tape in the early part of the incident happens to record something along the lines of ' I am going to try and get out of this icing' or ' jeez, have you seen the height, how did that happen' the mystery of what was intended evaporates. Mind you, that sort of clarity may also be the reason the CVR hasn't been reported in full at this stage.