Is it allowed to use the auto claim script ?
Correct. It is also not permitted to refer yourself. I can't think why else a question about botting a faucet would come from the referrer.
It is obviously allowed, because if you click on the faucet the admin pointed a message saying "Please click the ROLL button to WIN UP TO $200 IN FREE BITCOINS EVERY HOUR!" - short: "Please click the ROLL button EVERY HOUR!"
So how could you do this as a normal human being? Refusing to sleep? Nah. This is the proof it is allowed to let your chinese exchange student click it every hour...
Nobody in their right mind would interpret that as permission to violate the rules. It is clearly stated in the site's terms of service that you are not allowed to use bots.