I'm going to assume the answer the follow question is NO, but here goes, (and I thought this was asked before, but cannot find it)
TAG 'attacks' as per BMM (pg 17) and conversely TW
TAG DESIGNATION
If using target acquisition gear (TAG; see p. 113), all ’Mechs making attempts to designate a target do so after the end of the Movement Phase, but before the beginning of the Weapon Attack Phase (Initiative order is still followed, however).
Therefore, because TORSO TWISTING occurs at the start of the WEAPON ATTACK PHASE (TW page 37/BMM page 10), and TAG is end of Movement phase, TAG does not get to torso twist.