Yes you can add vinegar to your carpet cleaners reservoir and clean your carpets naturally using just vinegar and water.
You can also add some baking soda to the vinegar and water in your carpet cleaner which can help to deodorize your carpets.
I do this all the time when cleaning my carpets when I just need to clean the carpet however if you have a more severe stain then you may need to use regular carpet cleaner cleaning agents to get the stains out but overall vinegar and baking soda works great for cleaning and deodorizing carpets.