Not clear on your question. Are you asking if the other guy's insurance will pay for you to drive a rental car, or are you asking if they will pay the insurance to cover you in an accident (should one happen) while driving the rental ?
I would contact whomever you are working with on the claim and ask about them covering the cost of a rental. Usually they do for the amount of time it is estimated it will take for your repair to be done. If you are still driving your truck, they will only pay for the amount of time it is necessary for the actual repair work to be done.