Not sure how big a role this might actually play in the results.
For example, instead of asking kids "do you smoke pot?" you ask that of 80% of people and the other 20% get "do you own a dog?"; the surveyor has no idea which question was asked but knows the overall population of dog owners.
Does this technique have a name that you know of and did you consider it?
However, I can't remember the name of it, nor the article I read about it, and Google isn't helping.
Obviously, this would only be helpful if you don't have a good idea of how many people would lie in the first place. It also depends on the assumption that people won't lie given this plausible deniability.
The biggest problem I see is that this could only increase the variance of your survey results. The way I see it you have three binomial distributions base on three random variables:
1. The number of people who would answer yes to the survey question if they were honest.
2. The number of people who lied. (This is clearly not independent to the first random variable)
3. The number of people who flipped heads. (This clearly is independent)
I still really like this method since the increased variance is a moot point if giving people plausible deniability is the best way to normalize for lying. And you can always increase your confidence in the resulting proportion by increasing your sample size.
It would be interesting to run anonymized and non-anonymized surveys with the coin flip and without to try to determine how much anonymization reduces lying on various survey questions.
One nitpick: You should subtract 50% from the yes count and then multiply by two. So in your example, you would expect that 20% of those surveyed truly sexted or use drugs.