In most cases yes, you will be able to get a rental car after your car has been damaged in a wreck.
If your car is not a total loss and can be repaired, the negligent party who caused your wreck is obligated to pay you for what lawyers call "loss of use." That is simply payment for the period of time you are without the use of your car while your car is being repaired. The amount you can recover for this loss of use is the fair market value of the use of a car of the same make, model and kind as your car.
In virtually every case, insurance companies satisfy their obligation to pay for the loss of use of your damaged car by providing you a rental car which is of a similar model as yours.
If your car is a total loss, the law does not require the negligent party or its insurance company to provide you with a car rental. This is because the law in North Carolina provides that when there is a total loss of your car, the obligation of the negligent party is to pay you the difference between the fair market value of your vehicle immediately before the collision, and the fair market value of your care immediately after the collision. That is just as the car sits in the middle of the road without repair. The reasoning behind this law is that the negligent party is required to give you back the value of what he or she has taken away from you because of their negligence. Once they give you the value of your car, the negligent party is not obligated to provide you for loss of use of your car since, theoretically, your car was a total loss and therefore there is no loss of use for which you can collect.
Even though the law does not require insurance companies to pay for loss of use, in almost every case, insurance companies do provide a rental car to those owners whose vehicles have been totally damaged in the collision.
I have never known for sure why insurance companies are willing to do more than the law requires by providing rental cars to owners whose cars have been totally damaged. Insurance companies are not in the habit of paying more money than they have to pay.
I suppose the reason they voluntarily pay for a rental car is that it makes their task of settling the claim easier. It is easier to settle the claim with a car owner who feels they have been treated fairly by the insurance company. If insurance companies did not provide these rentals, it would surely be more difficult for them to arrive at a settlement for the total value of the car.