What does happen is the cumulative effect of those ads put your brand (coke) top of mind. Later when somebody is searching for "snacks" on google and paid search ad comes up, that person is more likely to chose Coke than RC Cola.
You need to look at effect your "brand" advertising is having on your paid search conversion rates. The industry is trying to solve this with "attribution" schemes ie figure out which ads every converted person has seen. (shameless-plug) But my company, Optimine has a much cooler and simpler approach using incremental modeling.
Here is a white paper that I think does a decent job of explaining. http://optimine.com/assets/pdfs/Measuring_Cross_Channel_Valu...