New Scientist and BBC have done pieces on this. And certainly DNA from a person with a transplant can and often does contain misleading signitures. Including a jail stretch for one guy who's brother had donated a kidney and also done the murder.

The one instance that springs to mind was a virtually TT lady who came out of hospital and straight into a pub for a beer (lager actually). When the history was revealed (there are ways in the USA apparently) the donor (or doner if you prefer) was a regular (daily) lager drinker.
The strength of the feelings vary from patient to patient.