Not to any appreciable amount. Unlike an open differential, Its torque biasing will allow greater than 50% of the torque coming down the drive shaft to be delivered to a single axle shaft. However, since you're on the road and since torque biasing doesn't occur until there is wheel slippage, the only way you're going to deliver high torque loads to a single shaft is to get one tire spinning on snow and the other coming into contact with pavement - and giving it some go pedal - street driving with a TrueTrac generally won't push any more torque down a shaft than an open differential.

One exception: Turning sharp corners will engage torque biasing as well, delivering a proportionally higher load to the inner wheel than to the outer. So if you have enough motor and enough traction, and not enough axle, you could potentially snap a shaft when turning where you might not necessarily do it with an open differential.

In a nut shell, take it easy and you'll never have a problem.