It's not that the front is getting "more" power. The split is always 65/35. Normally in a turn the coupler would slip allowing the front and rear to turn at different speeds, but after you get it really hot, then it won't let it slip as much so it feels like your getting more power to the front but in reality the power is the same. And that's only going to happen at really low speeds, at higher speeds with more power going through the coupler it will still slip unless your beating the crap out of it and getting things super hot.
As far as you peeling out, yeah it can be possible for a split second under the right conditions, the rear tires on a slick surface, and the front tires on a sticky surface. Mashing the gas will let the coupler slip and the rear tires spin for a split second, it's not like your able to do a burnout.