Yes, however, you should be sure to secure a general release of your liability from the injured party when you have made payment. I suggest you make all payments by check so that you have a written record of the payments.
Mr. Lundeen is licensed to practice law in Florida and Vermont. The response herein is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that, if known, could significantly change the reply and make it unsuitable. Mr. Lundeen strongly advises the questioner to confer with an attorney in your state in order to insure proper advice is received.
Paying a claim yourself rarely works in real life. Because the amount of damages claimed by the other side are usually more than someone without insurance can reasonably pay. However, if you have the money be sure to get a release. It would also be wise to have an attorney negotiate with the other side to make sure you don't over pay and that you get a proper release.
However it is more likely that they will settle with their insurance company directly, and then they will contact you to discuss you paying them. At that time you should obtain an attorney to negotiate on your behalf if possible.