Yes. The more content you have in a page, the more bandwidth it will use. People is not going to stay at your site (if it is a faucet) for long. So there is no need for Javascript or big images or special effects. Just something simple will do.
For my site (
http://bitrevenues.com), a custom script .. the cheapest plan at Namecheap (accept Bitcoin) do the job at just 9.88 USD for this first year. I just switched my host from Namecheap to SteadyTurtle - because my contract expired - and I think that SteadyTurtle cheapest plan will also do the job for a small faucet.
As for gambling site, I do not have the answer since I do not own one. However I would guess that the bandwidth use will be much bigger than a simple faucet.