Yes, it is possible for the police to charge you with a breathalyzer refusal even if you tried to blow into the device. If the police officer believes that you did not provide an adequate sample of your breath, they can still charge you with a refusal. In some cases, this may be because the person was unable to provide a deep enough breath or because they were breathing too quickly.
In order to avoid this situation, it is important to take your time when blowing into the breathalyzer and ensure that you are providing a deep enough sample of your breath. Additionally, make sure to follow any instructions given by the police officer administering the test so that they do not believe that you are intentionally refusing to comply.