Well, the short answer is "no"... the long answer is a bit more complicated.
First, there is the gravestone database at gardur.is - it is fragmentary - contains only a part of the cemetaries in Iceland.
Second, the
www.islendingabok.is database has much of this info, but that is only open to people in Iceland.
Third, all deaths since 1957 (or so) are available as public records they used to publish them in book format until a few years ago, but I think they are only releasing them electronically now.
Fourth, there is a database with most deaths from church records before 1870 or so-however, it has so many errors that I really do not want to recommend it to anyone.