It does not always take a while for a body to come to the surface and float. When the Aegis shot down Iran Air in the Persian Gulf, some of the bodies floated on the surface immediately.
As for current drift, here is the plot of the last body recovered and wreckage recovered on that day (June 17).
Here is the surface current for a five day period centered on June 17, 2009, using NOAA/NASA satellite observations (OSCAR) to generate the chart.
To me, there looks to be a pretty fair correlation between the surface currents and the plot for recovery of the objects and body. I'll leave the calculation of Reynolds numbers for a human body half-floating on the surface to others.
The 45 day meteorology for the closest buoy (0N, 35W) can be found here:
http://www.ndbc.noaa.gov/data/realtime2/31001.drift