That is a very vague question. In what context would the conga player be playing in? If the musical style is rumba or some other distinctively Afro-Cuban style then the "conga player" would have the advantage. It's important to note the distinction between "conga player" and "conguero".
If the musical style being played is West African, particularly from the areas populated by the Pulaar (Peul), Mandinque, and many other ethnic groups who have developed their traditional music over centuries, the "conga player would likely feel left out. Especially in ballet or group where there are several djembes, dununs and other instruments playing. I don't think the congas would even be heard over the djembes, however, a skilled conguero would be able to play something within the polyrhythmic structure that the West African music is based on.
There are numerous videos on YouTube where there are conga/djembe duets like this one
http://www.youtube.com/watch?v=F1ytxtTx1Pc that are amazing to watch. The Seck brothers are from Senegal (I don't know which ethnicity) which is a country with very diverse musical influences, including Latin and Caribbean, and there are several bands like Africando that play a crossover of Latin and traditional styles.
"One question remains: Is a technically savvy conga player at an advantage over the newbie when he sits down (or stands up with) a djembe?"
Your remaining question cannot truly be answered in my opinion. What do you mean by advantage? Can a trombone player have an advantage over a trumpet player? An electric guitar player over a banjo player? Do you see what I am getting at? It's not a simple yes or maybe question.
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