no, you regroup after you completed your burst of strenght (which includes drawing cards). Remember that you cannot play cards you drew on the same turn.
Neither taking up your cards nor regrouping is part of burst of strength.
Page 3 of the rules clearly states about drawn cards: "He may look at them and add them to his hand only after he has finished 'Burst of stength'."
So the timing question remains open in my point of view.