Thats a good question! Though the simple answer here is no, but the implications are interesting....
The Quadratrack and Full Time systems you are referring to basically deal with the "centre differential" i.e. speed / torque differences between the front and the back diffs. The discussion to date here has referred to lockers/ limited slip mechanisms on the rear differential only which focus on speed differences between the rear two tires only.....
Since we have the 4wd engaged in most of the cases discussed above, with large majority of manual TLC transmissions, you have the centre diff in a "locked" mode, always. Essentially when there is no gear selection for a centre diff (either by lever or button) on Toyota 4x4s it means that your centre diff is locked when you shift into 4x4. Hence in the above cases, with rear diff locked, essentially three tires on the vehicle will turn together i.e. two rear and either one at the front!
The full times systems work in various ways to either lock the centre diff when it senses slip in either front or back axles or in some "intelligent" cases to regulate torque away from the axle that is slipping towards the one that has traction. I believe the Quadratrack and TLC80 systems work to lock the centre diff based on a heat sensing mechanism (whatever its called) while I used to understand that the Pajero INVECS system works on the intelligent type mechanism....
I am not fully certain if I am correct on the INVECS mechanism but if that is the case, this would be an area where the Pajeros and the Evos have a distinct handling advantage over the field when running in 4wd unlocked mode. The only other comparable car on the local rally field is the post 2003 Surf which I understand employs a TORSEN LSD on the centre diff. Not sure if all models have it as YaserAG was not fully certain on his Surf...
PS: Sometimes I do wish MitsuMan was still alive on PW 
Then I realize what chit he would stir up if he ever realized that SK is admitting that 20th century Mitsu systems were superior to most modern Toys 
