The short answer is yes, the long answer is it depends. There are different grades of silicone rings. Look for silicone rings made with food-grade quality silicone . Food-grade silicone can be exposed to food (for example think of the silicone spatulas used for cooking), so exposure to alcohol-based liquids is generally safe.
Some lower quality grade silicone can be damaged by exposure to hand sanitizer and other alcohol-based liquids, losing their elasticity. Some flexible rings - especially ones wrapped in colourful design prints - are not made of silicone. It's best to ask the company to confirm if hand sanitizer will damage those rings.
To learn how to maximize the longevity of your silicone rings, check out Complete Guide to Silicone Ring Care.