From what reading and research I have done the 4WD versions do NOT have a LSD in the rear, only the 2WD versions have that. *See Toyota's web site for what is std for quick ref.*
Both 2WD & 4WD have VSC & TRAC (4WD also has A-TRAC only in 4L)
1st off I was surprised (before I purchased) to find out that the 4WD did not have a LSD, I guess they figure with TRAC & A-TRAC they did not need to use a LSD in the 4WD models, maybe it would 'fight' A-TRAC, dont know. My old SUV was 4WD w/ LSD in the rear.
I think someone would need to call Toyota to find out what the tolerance of TRAC is, how much faster does one tire have to spin than the other to activate the system. Think about it people, when you turn around a corner, even at 30mph, your 2 rear tires are going to spinning at different rates yet TRAC does not kick on. Now the question is....is the system smart enough to sense/measure steering (knowing you are turning) sensing the differences but not activating the system because of that. Who know what would happen when the wheel is straight. I know that VSC DOES measure the position of the steering in regards to all the sensors so it knows when to activate, not a far stretch to think that it is also linked to TRAC as well.
Correct me if I am wrong here, but I beleive TRAC is also linked to the differences between front and rear wheel spin/speed. Hense when in the snow/sand (*in 2WD*) and you give it too much gas and the rears spin at the same rate the system will still activate because it knows the fronts are not, indicating an issues to the 4R and activating TRAC to cut back.
If you run a smaller spare, turn off TRAC/VSC you should not have a single problem, since these 4WD's do not have a LSD either.
Like I said, I think we would need to find out the tolerances of the system to get a full idea of whether or not the system would need to be deactivated with a small spare.