Yes you can make money from a faucet contrary to what some here may lead you to believe. There are a large number of sites that make it without adsense. However do not expect to make very much right off the bat as your true value to advertisers can only be determined by the number of active members you have each day and how many claims they make per day.
Some sites even add Pop under ads to help generate some income. However some get real stupid and add more then 1 per claim which ends up ticking off more members then it helps. Solvemedia also helps generate some income for your site based on how many captcha are completed in a day.
BlockAdz which is operated by the Bitcoin Alien group has a pop under option and also allows you to setup a coupon code to give your advertisers a discount.
Feel free to PM if you have any questions or would like to talk more about this subject in more detail.