Since "TWS" is not Tracking while scan in Russian planes, it is not possible. Many times SNP and TWS are treated as the same, they are absolutely different. I could be probably called "Measure while search" because the box locked on a specific target only gives more detailed information about it, and does not tracking it. Therefore, if a bandit moves out of the radar's current sight, you loose the target. So there is NO tracking in the specific target. And as you said, SNP only gives you a greater situational awareness.
Anyway, if the boxed target get within the 75% (or so..) of the selected weapon's range, the radar automatically switches to single target track.