The danger with tactics like this is that the customers don't overthink tipping as much as the service staff, particularly if they are from a different country/culture. I tried to tip about $1/drink in New York, but when I got a free drink ("for being stuck" - volcano) I didn't know whether I was expected to tip the value, tip a little extra, or just take it as a favour. I would guess that on a bill, rather than a free drink, there's a good chance that people don't realise as well.
You should always tip the free drink. When you are in a bar or restaurant, you're receiving two things: the product and the service. When the product is free, you should still pay for the service.
