Avidin (a protein in egg whites) does bind biotin, and can reduce its absorption and lead to deficiency (well documented in nutrition literature). BUT - you'd need to eat a lot of raw egg whites for this to happen. In many of the studies, animals got ALL their protein from the egg whites.
More relevant: raw eggs can be sources of bacteria, most notably Salmonella. A number of Salmonella outbreaks have been traced to raw eggs. Organic or free range produced eggs may be less likely to have this problem, but they can still harbor pathogens.
As far as bioavailability goes, there isn't much hard data here. I cook mine, but that as much because of personal taste as anything else.