Looks like it charges you regardless, which is fine because it makes it "legitimate".
(you need an account to see links)
We received a tip from Moosa that the quickest way to do this is to bet 1 Neopoint, then wait for the eggs to hatch and hit the refresh button at the results page if you don't win. Doing this will generate a new, random set of 10 eggs to hatch while keeping the eggs you picked from the previous round. This isn't against the rules as you will still be charged for each time you refresh, it's just quicker than going through the whole process over and over.